Pub Date : 2021-12-21DOI: 10.1080/15326349.2021.2005628
E. T. Kolkovska, José Alfredo López Mimbela, José Hermenegildo Ramírez González
Abstract Let be a generating function, where are nonnegative measurable functions, and let be a continuous function. We prove that reaction-diffusion equations of the prototype possess nontrivial positive global solutions under suitable assumptions on and
{"title":"Existence of global solutions of a nonautonomous semilinear equation with varying reaction","authors":"E. T. Kolkovska, José Alfredo López Mimbela, José Hermenegildo Ramírez González","doi":"10.1080/15326349.2021.2005628","DOIUrl":"https://doi.org/10.1080/15326349.2021.2005628","url":null,"abstract":"Abstract Let be a generating function, where are nonnegative measurable functions, and let be a continuous function. We prove that reaction-diffusion equations of the prototype possess nontrivial positive global solutions under suitable assumptions on and","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"219 - 231"},"PeriodicalIF":0.7,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46355806","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 : 2021-12-19DOI: 10.1080/15326349.2021.2006066
N. Brites, C. Braumann
Abstract We can describe the size evolution of a harvested population in a randomly varying environment using stochastic differential equations. Previously, we have compared the profit performance of four harvesting policies: (i) optimal variable effort policy, based on variable effort; (ii) optimal penalized variable effort policies, penalized versions based on including an artificial running energy cost on the effort; (iii) stepwise policies, staircase versions where the harvesting effort is determined at the beginning of each year (or of each biennium) and kept constant throughout that year (or biennium); (iv) constant harvesting effort sustainable policy, based on constant effort. They have different properties, so it is also worth looking at combinations of such policies and studying the single and cross-effects of the amount of penalization, the absence or presence and type of steps, and the restraints on minimum and maximum allowed efforts. Using data based on a real harvested population and considering a logistic growth model, we perform such a comparison study of pure and mixed policies in terms of profit, applicability, and other relevant properties. We end up answering the question: is the optimal enemy of the good?
{"title":"Harvesting optimization with stochastic differential equations models: is the optimal enemy of the good?","authors":"N. Brites, C. Braumann","doi":"10.1080/15326349.2021.2006066","DOIUrl":"https://doi.org/10.1080/15326349.2021.2006066","url":null,"abstract":"Abstract We can describe the size evolution of a harvested population in a randomly varying environment using stochastic differential equations. Previously, we have compared the profit performance of four harvesting policies: (i) optimal variable effort policy, based on variable effort; (ii) optimal penalized variable effort policies, penalized versions based on including an artificial running energy cost on the effort; (iii) stepwise policies, staircase versions where the harvesting effort is determined at the beginning of each year (or of each biennium) and kept constant throughout that year (or biennium); (iv) constant harvesting effort sustainable policy, based on constant effort. They have different properties, so it is also worth looking at combinations of such policies and studying the single and cross-effects of the amount of penalization, the absence or presence and type of steps, and the restraints on minimum and maximum allowed efforts. Using data based on a real harvested population and considering a logistic growth model, we perform such a comparison study of pure and mixed policies in terms of profit, applicability, and other relevant properties. We end up answering the question: is the optimal enemy of the good?","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"41 - 59"},"PeriodicalIF":0.7,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48016426","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 : 2021-12-18DOI: 10.1080/15326349.2022.2066131
Miguel González, Pedro Martín-Chávez, I. D. del Puerto
Abstract A controlled branching process (CBP) is a modification of the standard Bienaymé–Galton–Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random number of initial individuals. The main aim of this article is to provide a Feller diffusion approximation for critical CBPs. A similar result by considering a fixed number of initial individuals by using operator semigroup convergence theorems has been previously proved by Sriram et al. (Stochastic Processes Appl. 2007;117:928–946). An alternative proof is now provided making use of limit theorems for random step processes.
{"title":"Diffusion approximation of controlled branching processes using limit theorems for random step processes","authors":"Miguel González, Pedro Martín-Chávez, I. D. del Puerto","doi":"10.1080/15326349.2022.2066131","DOIUrl":"https://doi.org/10.1080/15326349.2022.2066131","url":null,"abstract":"Abstract A controlled branching process (CBP) is a modification of the standard Bienaymé–Galton–Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random number of initial individuals. The main aim of this article is to provide a Feller diffusion approximation for critical CBPs. A similar result by considering a fixed number of initial individuals by using operator semigroup convergence theorems has been previously proved by Sriram et al. (Stochastic Processes Appl. 2007;117:928–946). An alternative proof is now provided making use of limit theorems for random step processes.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"232 - 248"},"PeriodicalIF":0.7,"publicationDate":"2021-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47242784","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 : 2021-12-02DOI: 10.1080/15326349.2022.2043166
S. Hautphenne, Minyuan Li
Abstract We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a continuous-time version of these processes, called total-progeny-dependent birth-and-death processes, and study some of their properties through the analysis of their deterministic (fluid) approximation. These properties include the maximum population size, the total progeny size at extinction, the time to reach the maximum population size, and the time until extinction. As the fluid approximation does not allow us to determine the time until extinction directly, we propose several methods to complement this approach. We also use the deterministic approach to study the behavior of the processes as we increase the magnitude of the individual’s birth rate.
{"title":"A fluid approach to total-progeny-dependent birth-and-death processes","authors":"S. Hautphenne, Minyuan Li","doi":"10.1080/15326349.2022.2043166","DOIUrl":"https://doi.org/10.1080/15326349.2022.2043166","url":null,"abstract":"Abstract We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a continuous-time version of these processes, called total-progeny-dependent birth-and-death processes, and study some of their properties through the analysis of their deterministic (fluid) approximation. These properties include the maximum population size, the total progeny size at extinction, the time to reach the maximum population size, and the time until extinction. As the fluid approximation does not allow us to determine the time until extinction directly, we propose several methods to complement this approach. We also use the deterministic approach to study the behavior of the processes as we increase the magnitude of the individual’s birth rate.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"80 - 103"},"PeriodicalIF":0.7,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44712193","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 : 2021-10-20DOI: 10.1080/15326349.2021.1987264
Arindam Panja, Pradip Kundu, B. Pradhan
Abstract In this paper, we establish some stochastic comparison results for two finite mixture models where the corresponding random variables follow one of the parental families of distributions, namely, proportional odds, proportional hazards, and proportional reversed hazards. The results of this paper are illustrated with numerical examples.
{"title":"On stochastic comparisons of finite mixture models","authors":"Arindam Panja, Pradip Kundu, B. Pradhan","doi":"10.1080/15326349.2021.1987264","DOIUrl":"https://doi.org/10.1080/15326349.2021.1987264","url":null,"abstract":"Abstract In this paper, we establish some stochastic comparison results for two finite mixture models where the corresponding random variables follow one of the parental families of distributions, namely, proportional odds, proportional hazards, and proportional reversed hazards. The results of this paper are illustrated with numerical examples.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"190 - 213"},"PeriodicalIF":0.7,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48578230","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 : 2021-10-17DOI: 10.1080/15326349.2021.1985520
Xiaowei Chen, F. Huang, Xiufang Li
Abstract This article describes a robust continuous-time asset-liability management problem under Markov regime-switching. First, we employ the “homothetic robustness” to preserve the performance of robustness for the ALM model, which runs well in precisely modified state variables and performs reasonably if some forms of model misspecification exist. Second, we consider the asset-to-liability ratio instead of the surplus, which ensures that we use relative values instead of absolute values to modify the wealth process. Besides, we use the stochastic dynamic programming method to get some closed-form results and analyze the impacts of parameters on the investment strategy and value function, respectively, by numerical examples.
{"title":"Robust asset-liability management under CRRA utility criterion with regime switching: a continuous-time model","authors":"Xiaowei Chen, F. Huang, Xiufang Li","doi":"10.1080/15326349.2021.1985520","DOIUrl":"https://doi.org/10.1080/15326349.2021.1985520","url":null,"abstract":"Abstract This article describes a robust continuous-time asset-liability management problem under Markov regime-switching. First, we employ the “homothetic robustness” to preserve the performance of robustness for the ALM model, which runs well in precisely modified state variables and performs reasonably if some forms of model misspecification exist. Second, we consider the asset-to-liability ratio instead of the surplus, which ensures that we use relative values instead of absolute values to modify the wealth process. Besides, we use the stochastic dynamic programming method to get some closed-form results and analyze the impacts of parameters on the investment strategy and value function, respectively, by numerical examples.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"167 - 189"},"PeriodicalIF":0.7,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44383383","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 : 2021-10-13DOI: 10.1080/15326349.2021.1982394
Dai Katoh, S. Shioda
Abstract The consensus attained in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the probability laws of the consensus in a broadcast-based consensus-forming algorithm. First, we derive a fundamental equation on the time evolution of the opinions of agents. From the derived equation, we show that the consensus attained by the algorithm is given as a fixed-point solution of a linear equation. We then focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus with an algorithm for computing the distribution function of the consensus numerically. In the infinite-number-of-agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a Lévy distribution.
{"title":"Probability laws of consensus in a broadcast-based consensus-forming algorithm","authors":"Dai Katoh, S. Shioda","doi":"10.1080/15326349.2021.1982394","DOIUrl":"https://doi.org/10.1080/15326349.2021.1982394","url":null,"abstract":"Abstract The consensus attained in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the probability laws of the consensus in a broadcast-based consensus-forming algorithm. First, we derive a fundamental equation on the time evolution of the opinions of agents. From the derived equation, we show that the consensus attained by the algorithm is given as a fixed-point solution of a linear equation. We then focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus with an algorithm for computing the distribution function of the consensus numerically. In the infinite-number-of-agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a Lévy distribution.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"91 - 115"},"PeriodicalIF":0.7,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45127903","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 : 2021-10-05DOI: 10.1080/15326349.2021.1975548
Suyono, Ibnu Hadi, Mulyono
Abstract Consider an alternating renewal process that, over time, alternates between two states (up and down), starting in upstate at time 0. Associated with each up interval a reward which is a function of the interval length. Similarly, we associate with each down interval a reward which depends on the length of it through some function. We call the total reward earned in the time interval an instantaneous alternating renewal reward process. In this article, we derive the probability distribution of the total reward and its expected value. The results are presented in the form of Laplace transforms.
{"title":"Alternating renewal processes with instantaneous rewards","authors":"Suyono, Ibnu Hadi, Mulyono","doi":"10.1080/15326349.2021.1975548","DOIUrl":"https://doi.org/10.1080/15326349.2021.1975548","url":null,"abstract":"Abstract Consider an alternating renewal process that, over time, alternates between two states (up and down), starting in upstate at time 0. Associated with each up interval a reward which is a function of the interval length. Similarly, we associate with each down interval a reward which depends on the length of it through some function. We call the total reward earned in the time interval an instantaneous alternating renewal reward process. In this article, we derive the probability distribution of the total reward and its expected value. The results are presented in the form of Laplace transforms.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"51 - 69"},"PeriodicalIF":0.7,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44086427","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 : 2021-09-26DOI: 10.1080/15326349.2021.1977141
Matheus B. Guerrero, W. Barreto‐Souza, H. Ombao
Abstract Integer-valued autoregressive (INAR) processes are generally defined by specifying the thinning operator and either the innovations or the marginal distributions. The major limitations of such processes include difficulties in deriving the marginal properties and justifying the choice of the thinning operator. To overcome these drawbacks, we propose a novel approach for building an INAR model that offers the flexibility to prespecify both marginal and innovation distributions. Thus, the thinning operator is no longer subjectively selected but is rather a direct consequence of the marginal and innovation distributions specified by the modeler. Novel INAR processes are introduced following this perspective; these processes include a model with geometric marginal and innovation distributions (Geo-INAR) and models with bounded innovations. We explore the Geo-INAR model, which is a natural alternative to the classical Poisson INAR model. The Geo-INAR process has interesting stochastic properties, such as MA( ) representation, time reversibility, and closed forms for the -order transition probabilities, which enables a natural framework to perform coherent forecasting. To demonstrate the real-world application of the Geo-INAR model, we analyze a count time series of criminal records in sex offenses using the proposed methodology and compare it with existing INAR and integer-valued generalized autoregressive conditional heteroscedastic models.
{"title":"Integer-valued autoregressive processes with prespecified marginal and innovation distributions: a novel perspective","authors":"Matheus B. Guerrero, W. Barreto‐Souza, H. Ombao","doi":"10.1080/15326349.2021.1977141","DOIUrl":"https://doi.org/10.1080/15326349.2021.1977141","url":null,"abstract":"Abstract Integer-valued autoregressive (INAR) processes are generally defined by specifying the thinning operator and either the innovations or the marginal distributions. The major limitations of such processes include difficulties in deriving the marginal properties and justifying the choice of the thinning operator. To overcome these drawbacks, we propose a novel approach for building an INAR model that offers the flexibility to prespecify both marginal and innovation distributions. Thus, the thinning operator is no longer subjectively selected but is rather a direct consequence of the marginal and innovation distributions specified by the modeler. Novel INAR processes are introduced following this perspective; these processes include a model with geometric marginal and innovation distributions (Geo-INAR) and models with bounded innovations. We explore the Geo-INAR model, which is a natural alternative to the classical Poisson INAR model. The Geo-INAR process has interesting stochastic properties, such as MA( ) representation, time reversibility, and closed forms for the -order transition probabilities, which enables a natural framework to perform coherent forecasting. To demonstrate the real-world application of the Geo-INAR model, we analyze a count time series of criminal records in sex offenses using the proposed methodology and compare it with existing INAR and integer-valued generalized autoregressive conditional heteroscedastic models.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"70 - 90"},"PeriodicalIF":0.7,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46384180","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 : 2021-09-19DOI: 10.1080/15326349.2022.2047073
Vladimir Kutsenko, E. Yarovaya
Abstract We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous properties of a particle field, e.g., such as intermittency. However, the time intervals on which this intermittency phenomenon can be observed are very difficult to estimate in practice. In this paper, branching media containing only a finite and non-finite number of branching sources are considered. The evolution of the mean number of particles with a random point perturbation and one initial ancestor particle at a lattice point is described by an appropriate Cauchy problem for the evolutionary operator. We review some previous results about the long-time behavior of the medium-averaged moments for the particle population at every lattice point as well as the total one over the lattice and present an algorithm for the simulation of branching random walks under various assumptions about the medium, including the medium randomness. The effects arising in random non-homogeneous and homogeneous media are then compared and illustrated by simulations based on the potential with Weibull-type upper tail. A wide range of models under different assumptions on a branching medium, a configuration of branching sources, and a lattice dimension were considered during the comparison. The simulation results indicate that intermittency can be observed in random media even over finite time intervals.
{"title":"Symmetric branching random walks in random media: comparing theoretical and numerical results","authors":"Vladimir Kutsenko, E. Yarovaya","doi":"10.1080/15326349.2022.2047073","DOIUrl":"https://doi.org/10.1080/15326349.2022.2047073","url":null,"abstract":"Abstract We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous properties of a particle field, e.g., such as intermittency. However, the time intervals on which this intermittency phenomenon can be observed are very difficult to estimate in practice. In this paper, branching media containing only a finite and non-finite number of branching sources are considered. The evolution of the mean number of particles with a random point perturbation and one initial ancestor particle at a lattice point is described by an appropriate Cauchy problem for the evolutionary operator. We review some previous results about the long-time behavior of the medium-averaged moments for the particle population at every lattice point as well as the total one over the lattice and present an algorithm for the simulation of branching random walks under various assumptions about the medium, including the medium randomness. The effects arising in random non-homogeneous and homogeneous media are then compared and illustrated by simulations based on the potential with Weibull-type upper tail. A wide range of models under different assumptions on a branching medium, a configuration of branching sources, and a lattice dimension were considered during the comparison. The simulation results indicate that intermittency can be observed in random media even over finite time intervals.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"60 - 79"},"PeriodicalIF":0.7,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43418438","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：