Pub Date : 2022-05-20DOI: 10.1080/15326349.2022.2074458
Jacob Bergquist, K. Sigman
Abstract We analyze two nonwork-conserving variations of the M/G/1 preemptive last-in first-out (LIFO) queue with emphasis on deriving explicit expressions for the limiting (stationary) distributions of service times found in service by an arrival, workload and a variety of related quantities of interest. Workload is also used as a tool to derive the proportion of time that the system is busy, and stability conditions. In the first model, known as preemptive-repeat different (PRD), preempted customers are returned to the front of the queue with a new independent and identically distributed service time. In the second, known as preemptive-repeat identical (PRI), they are returned to the front of the queue with their original service time. Our analysis is based on queueing theory methods such as the Rate Conservation Law, PASTA, regenerative process theory and Little’s Law ( ). For the second model we even derive the joint distribution of age and excess of the service time found in service by an arrival, and find they are quite different from what is found in standard work-conserving models. We also give heavy-traffic limits and tail asymptotics for stationary workload for both models, as well as deriving an implicit representation for the distribution of sojourn time by introducing an alternative effective service time distribution.
{"title":"Stationary workload and service times for some nonwork-conserving M/G/1 preemptive LIFO queues","authors":"Jacob Bergquist, K. Sigman","doi":"10.1080/15326349.2022.2074458","DOIUrl":"https://doi.org/10.1080/15326349.2022.2074458","url":null,"abstract":"Abstract We analyze two nonwork-conserving variations of the M/G/1 preemptive last-in first-out (LIFO) queue with emphasis on deriving explicit expressions for the limiting (stationary) distributions of service times found in service by an arrival, workload and a variety of related quantities of interest. Workload is also used as a tool to derive the proportion of time that the system is busy, and stability conditions. In the first model, known as preemptive-repeat different (PRD), preempted customers are returned to the front of the queue with a new independent and identically distributed service time. In the second, known as preemptive-repeat identical (PRI), they are returned to the front of the queue with their original service time. Our analysis is based on queueing theory methods such as the Rate Conservation Law, PASTA, regenerative process theory and Little’s Law ( ). For the second model we even derive the joint distribution of age and excess of the service time found in service by an arrival, and find they are quite different from what is found in standard work-conserving models. We also give heavy-traffic limits and tail asymptotics for stationary workload for both models, as well as deriving an implicit representation for the distribution of sojourn time by introducing an alternative effective service time distribution.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"515 - 544"},"PeriodicalIF":0.7,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-01DOI: 10.1080/15326349.2022.2066130
M. Haviv, Yoav Kerner
Abstract We derive the mean waiting times in an M/G/1 priority queue when the decision who receives the current completed service (production) is determined at the end of the service period. We consider two variations of this scheme. The first is when the server works only when customers are present, while the second is when the server works on a nonstop basis but scraps its work if production is completed when there are no customers in line. We show that for the former variant (whose overall mean is as in the standard head-of-the-line (HOL) priority model), the gain from this scheme in comparison with the HOL case is monotone increasing with the priority level (being positive for the higher classes and negative for the lower classes).
摘要导出了M/G/1优先队列在服务周期结束时决定谁接收当前已完成的服务(生产)时的平均等待时间。我们考虑这个方案的两种变体。第一种情况是服务器只在客户在场的情况下工作，而第二种情况是服务器在不间断的基础上工作，但如果在没有客户排队的情况下完成生产，则丢弃其工作。我们表明，对于前一种变体(其总体平均值与标准的head-of- line (HOL)优先级模型一样)，与HOL情况相比，该方案的增益是单调的，随着优先级的增加而增加(对于较高的类别为正，对于较低的类别为负)。
{"title":"Queueing with priorities and standard service: Stoppable and unstoppable servers","authors":"M. Haviv, Yoav Kerner","doi":"10.1080/15326349.2022.2066130","DOIUrl":"https://doi.org/10.1080/15326349.2022.2066130","url":null,"abstract":"Abstract We derive the mean waiting times in an M/G/1 priority queue when the decision who receives the current completed service (production) is determined at the end of the service period. We consider two variations of this scheme. The first is when the server works only when customers are present, while the second is when the server works on a nonstop basis but scraps its work if production is completed when there are no customers in line. We show that for the former variant (whose overall mean is as in the standard head-of-the-line (HOL) priority model), the gain from this scheme in comparison with the HOL case is monotone increasing with the priority level (being positive for the higher classes and negative for the lower classes).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"503 - 514"},"PeriodicalIF":0.7,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43798461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-28DOI: 10.1080/15326349.2022.2066128
Lina Bian, G. Wang, Peng Liu
{"title":"Reliability analysis for systems with interactive competing degradation processes and mixed shock effects","authors":"Lina Bian, G. Wang, Peng Liu","doi":"10.1080/15326349.2022.2066128","DOIUrl":"https://doi.org/10.1080/15326349.2022.2066128","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45818031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-25DOI: 10.1080/15326349.2022.2093374
N. H. Nguyen, M. Kimmel
Abstract We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized by the mutation rate of the original cells and the survival probability of the altered cells’ progeny. For each system, we derive a closed-form expression for the joint probability generating function of cell counts, and perform asymptotic analysis on the behaviors of the cell population with particular focus on probability of extinction. Part of our results confirms known properties of branching processes using a different approach while other are original. While the model is best suited for modeling the fate of differentiating stem cells, we discuss other scenarios in which these system dynamics may be applicable in real life. We also discuss the history of the subject.
{"title":"Stochastic models of stem cells and their descendants under different criticality assumptions","authors":"N. H. Nguyen, M. Kimmel","doi":"10.1080/15326349.2022.2093374","DOIUrl":"https://doi.org/10.1080/15326349.2022.2093374","url":null,"abstract":"Abstract We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized by the mutation rate of the original cells and the survival probability of the altered cells’ progeny. For each system, we derive a closed-form expression for the joint probability generating function of cell counts, and perform asymptotic analysis on the behaviors of the cell population with particular focus on probability of extinction. Part of our results confirms known properties of branching processes using a different approach while other are original. While the model is best suited for modeling the fate of differentiating stem cells, we discuss other scenarios in which these system dynamics may be applicable in real life. We also discuss the history of the subject.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"249 - 264"},"PeriodicalIF":0.7,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43314445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-15DOI: 10.1080/15326349.2022.2063335
Y. Slaoui
Abstract In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set.
{"title":"Bernstein polynomial of recursive regression estimation with censored data","authors":"Y. Slaoui","doi":"10.1080/15326349.2022.2063335","DOIUrl":"https://doi.org/10.1080/15326349.2022.2063335","url":null,"abstract":"Abstract In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"462 - 487"},"PeriodicalIF":0.7,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44025412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-06DOI: 10.1080/15326349.2022.2055073
S. Yadav, A. Laha
Abstract Branching process and their variants are a widely used mathematical model in the study of population dynamics, in which all individuals in a given generation produces some random number of individuals for the next generation. In the recent past, branching process has also found applications in areas like operations research, marketing, finance, genetics etc. A problem that has caught attention in the context of coalescence in branching process is as follows: Assume that the branching process is started by one individual in 0th generation and the population size of the tree obtained by branching process in generation n is greater than 1. Next, pick two individuals from n th generation at random and trace their lines of descent back till they meet. Call that random generation by Xn . The objective is to study the properties of Xn . While this problem has been studied by many authors for simple and multitype discrete time branching processes, not much attention has been given for the realistic extension when one individual is allowed to survive for more than one generation and can also give birth more than once. We study this problem for some deterministic and random cases. Explicit expressions about some mathematical properties of Xn have been derived for broad classes of deterministic trees. For random trees, we provide explicit expression for some special cases. We also derive properties of Xn as n goes to infinity. Additionally, simulation analysis has also been performed and some interesting insights are discussed.
{"title":"Coalescence in branching processes with age dependent structure in population","authors":"S. Yadav, A. Laha","doi":"10.1080/15326349.2022.2055073","DOIUrl":"https://doi.org/10.1080/15326349.2022.2055073","url":null,"abstract":"Abstract Branching process and their variants are a widely used mathematical model in the study of population dynamics, in which all individuals in a given generation produces some random number of individuals for the next generation. In the recent past, branching process has also found applications in areas like operations research, marketing, finance, genetics etc. A problem that has caught attention in the context of coalescence in branching process is as follows: Assume that the branching process is started by one individual in 0th generation and the population size of the tree obtained by branching process in generation n is greater than 1. Next, pick two individuals from n th generation at random and trace their lines of descent back till they meet. Call that random generation by Xn . The objective is to study the properties of Xn . While this problem has been studied by many authors for simple and multitype discrete time branching processes, not much attention has been given for the realistic extension when one individual is allowed to survive for more than one generation and can also give birth more than once. We study this problem for some deterministic and random cases. Explicit expressions about some mathematical properties of Xn have been derived for broad classes of deterministic trees. For random trees, we provide explicit expression for some special cases. We also derive properties of Xn as n goes to infinity. Additionally, simulation analysis has also been performed and some interesting insights are discussed.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"104 - 117"},"PeriodicalIF":0.7,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48088010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-04DOI: 10.1080/15326349.2022.2049822
Ann M. Noblesse, Nikki Sonenberg, R. Boute, M. Lambrecht, B. Van Houdt
Abstract In this paper we analyze a continuous review finite capacity production-inventory system with two products in inventory. With stochastic order quantities and time between orders, the model reflects a supply chain that operates in an environment with high levels of volatility. The inventory is replenished using an independent order-up-to (s, S) policy or a can-order (s, c, S) joint replenishment policy in which the endogenously determined lead times drive the parameters of the replenishment policy. The production facility is modeled as a multi-type MMAP[K]/PH[K]/1 queue in which there are K possible inventory positions when the order is placed and the age process of the busy queue has matrix-exponential distribution. We characterize the system and determine the steady state distribution using matrix analytic methods. Using numerical methods we obtain the inventory parameters that minimize the total ordering and inventory related costs. We present numerical comparisons of independent and joint replenishment policies with varying lead times, order quantities, and cost reductions. We further demonstrate the interplay between the two products in terms of lead times, order quantities and costs.
{"title":"A joint replenishment production-inventory model as an MMAP[K]/PH[K]/1 queue","authors":"Ann M. Noblesse, Nikki Sonenberg, R. Boute, M. Lambrecht, B. Van Houdt","doi":"10.1080/15326349.2022.2049822","DOIUrl":"https://doi.org/10.1080/15326349.2022.2049822","url":null,"abstract":"Abstract In this paper we analyze a continuous review finite capacity production-inventory system with two products in inventory. With stochastic order quantities and time between orders, the model reflects a supply chain that operates in an environment with high levels of volatility. The inventory is replenished using an independent order-up-to (s, S) policy or a can-order (s, c, S) joint replenishment policy in which the endogenously determined lead times drive the parameters of the replenishment policy. The production facility is modeled as a multi-type MMAP[K]/PH[K]/1 queue in which there are K possible inventory positions when the order is placed and the age process of the busy queue has matrix-exponential distribution. We characterize the system and determine the steady state distribution using matrix analytic methods. Using numerical methods we obtain the inventory parameters that minimize the total ordering and inventory related costs. We present numerical comparisons of independent and joint replenishment policies with varying lead times, order quantities, and cost reductions. We further demonstrate the interplay between the two products in terms of lead times, order quantities and costs.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"390 - 415"},"PeriodicalIF":0.7,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46919122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-25DOI: 10.1080/15326349.2022.2041037
Kaloyan N. Vitanov, M. Slavtchova-Bojkova
Abstract Biological populations under stress often face certain extinction unless they adapt toward unfavorable circumstances. In some scenarios such adaptation can assume the form of mutations within the genome of the population (e.g., cancer cells resisting chemotherapy, viruses developing resistance toward a vaccine), while in other scenarios adaptation can be in the form of movement toward some physical location (e.g., spreading of cancer cells to parts of the organism unaffected by treatment, animal populations fleeing polluted areas or areas struck by disaster). Regardless of the particular situation, it is often the case that cells/individuals with different levels of adaptation (which we may group into types) emerge among the cells/individuals of a stressed population. We propose a decomposable multi-type Sevastyanov branching process (possibly with multiple supercritical types) for modeling relevant aspects of the dynamics of such populations. The branching process developed within this paper is a generalization of the decomposable multi-type age-dependent branching process with a single supercritical type considered in Slavtchova-Bojkova and Vitanov. With respect to Slavtchova-Bojkova and Vitanov, we introduce additional, possibly supercritical, types into the interaction scheme between types, further, we incorporate possible dependence of the reproductive capabilities of cells/individuals from their age. We obtain a system of integral equations for the probability generating function of the new process and accordingly expand previous results from Slavtchova-Bojkova and Vitanov concerning probabilities of extinction, number of occurred mutations, waiting time to escape mutant, and immediate risk of escaping extinction. We also provide a general numerical scheme for calculating obtained systems of integral equations.
{"title":"Modeling escape from extinction with decomposable multi-type Sevastyanov branching processes","authors":"Kaloyan N. Vitanov, M. Slavtchova-Bojkova","doi":"10.1080/15326349.2022.2041037","DOIUrl":"https://doi.org/10.1080/15326349.2022.2041037","url":null,"abstract":"Abstract Biological populations under stress often face certain extinction unless they adapt toward unfavorable circumstances. In some scenarios such adaptation can assume the form of mutations within the genome of the population (e.g., cancer cells resisting chemotherapy, viruses developing resistance toward a vaccine), while in other scenarios adaptation can be in the form of movement toward some physical location (e.g., spreading of cancer cells to parts of the organism unaffected by treatment, animal populations fleeing polluted areas or areas struck by disaster). Regardless of the particular situation, it is often the case that cells/individuals with different levels of adaptation (which we may group into types) emerge among the cells/individuals of a stressed population. We propose a decomposable multi-type Sevastyanov branching process (possibly with multiple supercritical types) for modeling relevant aspects of the dynamics of such populations. The branching process developed within this paper is a generalization of the decomposable multi-type age-dependent branching process with a single supercritical type considered in Slavtchova-Bojkova and Vitanov. With respect to Slavtchova-Bojkova and Vitanov, we introduce additional, possibly supercritical, types into the interaction scheme between types, further, we incorporate possible dependence of the reproductive capabilities of cells/individuals from their age. We obtain a system of integral equations for the probability generating function of the new process and accordingly expand previous results from Slavtchova-Bojkova and Vitanov concerning probabilities of extinction, number of occurred mutations, waiting time to escape mutant, and immediate risk of escaping extinction. We also provide a general numerical scheme for calculating obtained systems of integral equations.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"161 - 184"},"PeriodicalIF":0.7,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49309950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-16DOI: 10.1080/15326349.2022.2045205
Nicolás Piña, T. Caraballo, E. Porcu
Abstract The paper provides conditions for the fractional Laplacian and its spectral representation on stationary Gaussian random fields to be well-defined. In addition, we study existence and uniqueness of the weak solution for a stochastic fractional elliptic equation driven by an additive colored noise over an open bounded set. Both spectral and variational approaches are used to provide a solution. Further, the functional covariance associated with the solution is derived.
{"title":"A stochastic fractional Laplace equation driven by colored noise on bounded domain, and its covariance functional","authors":"Nicolás Piña, T. Caraballo, E. Porcu","doi":"10.1080/15326349.2022.2045205","DOIUrl":"https://doi.org/10.1080/15326349.2022.2045205","url":null,"abstract":"Abstract The paper provides conditions for the fractional Laplacian and its spectral representation on stationary Gaussian random fields to be well-defined. In addition, we study existence and uniqueness of the weak solution for a stochastic fractional elliptic equation driven by an additive colored noise over an open bounded set. Both spectral and variational approaches are used to provide a solution. Further, the functional covariance associated with the solution is derived.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"365 - 389"},"PeriodicalIF":0.7,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47785015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-11DOI: 10.1080/15326349.2022.2032755
C. Gutiérrez, C. Minuesa
Abstract Two density-dependent branching processes are considered to model predator–prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each species is distributed according to a binomial distribution with size given by the species population size and probability of success depending on the density of preys per predator at the current generation. The difference between the two proposed processes lies in the food supply of preys. In the first one, we consider that preys have all the food they need at their disposal while in the second one, we assume that the natural resources of the environment are limited and therefore there exists a competition among preys for food supplies. Results on the fixation and extinction of both species as well as conditions for the coexistence are provided for the first model. On the event of coexistence of both populations and on the prey fixation event, the limiting growth rates are obtained. For the second model, we prove that the extinction of the entire system occurs almost surely. Finally, the evolution of both models over the generations and our analytical findings are illustrated by simulated examples.
{"title":"Predator–prey density-dependent branching processes","authors":"C. Gutiérrez, C. Minuesa","doi":"10.1080/15326349.2022.2032755","DOIUrl":"https://doi.org/10.1080/15326349.2022.2032755","url":null,"abstract":"Abstract Two density-dependent branching processes are considered to model predator–prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each species is distributed according to a binomial distribution with size given by the species population size and probability of success depending on the density of preys per predator at the current generation. The difference between the two proposed processes lies in the food supply of preys. In the first one, we consider that preys have all the food they need at their disposal while in the second one, we assume that the natural resources of the environment are limited and therefore there exists a competition among preys for food supplies. Results on the fixation and extinction of both species as well as conditions for the coexistence are provided for the first model. On the event of coexistence of both populations and on the prey fixation event, the limiting growth rates are obtained. For the second model, we prove that the extinction of the entire system occurs almost surely. Finally, the evolution of both models over the generations and our analytical findings are illustrated by simulated examples.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"265 - 292"},"PeriodicalIF":0.7,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42500876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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