Pub Date : 2022-11-07DOI: 10.1080/07362994.2022.2140677
M. N. Mishra, B. Prakasa Rao
Abstract We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth in the drift but the real model has a cusp-type singularity in the drift function and the driving force is a fractional Brownian motion.
{"title":"Estimation for misspecification when theoretical model for signal is smooth but real signal is of cusp-type and driven by a fractional Brownian motion","authors":"M. N. Mishra, B. Prakasa Rao","doi":"10.1080/07362994.2022.2140677","DOIUrl":"https://doi.org/10.1080/07362994.2022.2140677","url":null,"abstract":"Abstract We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth in the drift but the real model has a cusp-type singularity in the drift function and the driving force is a fractional Brownian motion.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44467825","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 : 2022-09-19DOI: 10.1080/07362994.2022.2121723
E. Appiah, G. S. Ladde, J. Ladde
Abstract In this work, an attempt is made to develop an innovative alternative stochastic interconnected hybrid dynamic model for time-to-event processes in a systematic and unified way. The procedure is composed of the following components: (1) development of a continuous-time state dynamic model, (2) formulation of an interconnected hybrid dynamic model composed of both continuous and discrete-time states of time-to-event processes, (3) derivation of conceptual computational interconnected dynamic algorithm for time-to-event data statistic, and (4) construction of conceptual and computational simulation dynamic procedure for state and parameter estimations. The development of the presented approach is motivated by parameter and state estimation of time-to-event processes in biological, chemical, engineering, epidemiological, medical, military, and social dynamic processes under the influence of discrete-time intervention processes. The presented algorithm is independent of any particular form of survival distributions or data sets. Moreover, it does not require a closed form survival function distributions. The introduction of intervention processes provides a measure of influence of new tools/procedures/approaches in continuous-time states of time-to-event dynamic process. In particular, it generates a measure of the degree of sustainability, survivability, reliability of a time-to-event process. In addition, intervention processes provide comparison between the past and currently used tools/procedures/approaches/etc. The developed procedure coupled with modified Local Lagged Adapted Generalized Method of Moments (LLGMM) approach also provides a measure of degree of confidence, prediction, and planning assessments.
{"title":"Stochastic interconnected hybrid dynamic modeling for time-to-event processes","authors":"E. Appiah, G. S. Ladde, J. Ladde","doi":"10.1080/07362994.2022.2121723","DOIUrl":"https://doi.org/10.1080/07362994.2022.2121723","url":null,"abstract":"Abstract In this work, an attempt is made to develop an innovative alternative stochastic interconnected hybrid dynamic model for time-to-event processes in a systematic and unified way. The procedure is composed of the following components: (1) development of a continuous-time state dynamic model, (2) formulation of an interconnected hybrid dynamic model composed of both continuous and discrete-time states of time-to-event processes, (3) derivation of conceptual computational interconnected dynamic algorithm for time-to-event data statistic, and (4) construction of conceptual and computational simulation dynamic procedure for state and parameter estimations. The development of the presented approach is motivated by parameter and state estimation of time-to-event processes in biological, chemical, engineering, epidemiological, medical, military, and social dynamic processes under the influence of discrete-time intervention processes. The presented algorithm is independent of any particular form of survival distributions or data sets. Moreover, it does not require a closed form survival function distributions. The introduction of intervention processes provides a measure of influence of new tools/procedures/approaches in continuous-time states of time-to-event dynamic process. In particular, it generates a measure of the degree of sustainability, survivability, reliability of a time-to-event process. In addition, intervention processes provide comparison between the past and currently used tools/procedures/approaches/etc. The developed procedure coupled with modified Local Lagged Adapted Generalized Method of Moments (LLGMM) approach also provides a measure of degree of confidence, prediction, and planning assessments.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44528510","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 : 2022-09-19DOI: 10.1080/07362994.2022.2123344
M. Abundo
Abstract We study the tail behavior of the distribution of the running maximum of a zero mean Gaussian Bridge obtained from a continuous Gaussian process X(t) with by conditioning X(t) to have the value zero at time T. Some explicit examples are shown.
{"title":"Asymptotic of the running maximum distribution of a Gaussian Bridge","authors":"M. Abundo","doi":"10.1080/07362994.2022.2123344","DOIUrl":"https://doi.org/10.1080/07362994.2022.2123344","url":null,"abstract":"Abstract We study the tail behavior of the distribution of the running maximum of a zero mean Gaussian Bridge obtained from a continuous Gaussian process X(t) with by conditioning X(t) to have the value zero at time T. Some explicit examples are shown.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46951057","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 : 2022-08-07DOI: 10.1080/07362994.2022.2104730
M. Jornet
Abstract In this article, we prove new results for the anticipating stochastic integral introduced by Ayed and Kuo. We present an existence criterion for the integral, a Fubini’s theorem, a Leibniz integral rule, and an alternative definition for a class of integrands.
{"title":"On the Ayed-Kuo stochastic integration for anticipating integrands","authors":"M. Jornet","doi":"10.1080/07362994.2022.2104730","DOIUrl":"https://doi.org/10.1080/07362994.2022.2104730","url":null,"abstract":"Abstract In this article, we prove new results for the anticipating stochastic integral introduced by Ayed and Kuo. We present an existence criterion for the integral, a Fubini’s theorem, a Leibniz integral rule, and an alternative definition for a class of integrands.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41787598","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 : 2022-08-05DOI: 10.1080/07362994.2022.2104314
J. Owo
Abstract In this paper, we investigate an existence of minimal (resp. maximal) solutions for backward doubly stochastic differential equations (BDSDEs, in short) when the coefficient with respect to the forward integral is left (resp. right)-continuous in y and continuous in z with stochastic linear growth in (y, z). Also, the associated comparison theorem is obtained.
{"title":"Backward doubly stochastic differential equations with discontinuous and stochastic linear growth generator","authors":"J. Owo","doi":"10.1080/07362994.2022.2104314","DOIUrl":"https://doi.org/10.1080/07362994.2022.2104314","url":null,"abstract":"Abstract In this paper, we investigate an existence of minimal (resp. maximal) solutions for backward doubly stochastic differential equations (BDSDEs, in short) when the coefficient with respect to the forward integral is left (resp. right)-continuous in y and continuous in z with stochastic linear growth in (y, z). Also, the associated comparison theorem is obtained.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48973588","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 : 2022-07-09DOI: 10.1080/07362994.2022.2093223
I. R. Sofia, M. Ghosh
Abstract In this study, we formulate and analyze a non-linear mathematical model to study the dynamics of smoking and its impact on society. This is a compartment model which has four compartments, namely, potential smoker, occasional smoker, smoker and quitters. As per WHO, each year there is a significant number of smoking-related deaths. Keeping this in view, we have incorporated smoking-related death in our proposed model. Further, we investigate the model for possible equilibria, compute the basic reproduction number and investigate the stability of obtained equilibria. Later we extend this model to stochastic model and perform numerical simulation for both the deterministic and the stochastic model. The results of stochastic model are almost similar to the results obtained for deterministic model. We have also explored the impact of the parameters related to quitting smoking habits on the equilibrium level of occasional smokers. We also perform sensitivity analysis to find the key parameters which make significant change in the reproduction numbers.
{"title":"Mathematical modeling of smoking habits in the society","authors":"I. R. Sofia, M. Ghosh","doi":"10.1080/07362994.2022.2093223","DOIUrl":"https://doi.org/10.1080/07362994.2022.2093223","url":null,"abstract":"Abstract In this study, we formulate and analyze a non-linear mathematical model to study the dynamics of smoking and its impact on society. This is a compartment model which has four compartments, namely, potential smoker, occasional smoker, smoker and quitters. As per WHO, each year there is a significant number of smoking-related deaths. Keeping this in view, we have incorporated smoking-related death in our proposed model. Further, we investigate the model for possible equilibria, compute the basic reproduction number and investigate the stability of obtained equilibria. Later we extend this model to stochastic model and perform numerical simulation for both the deterministic and the stochastic model. The results of stochastic model are almost similar to the results obtained for deterministic model. We have also explored the impact of the parameters related to quitting smoking habits on the equilibrium level of occasional smokers. We also perform sensitivity analysis to find the key parameters which make significant change in the reproduction numbers.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43987369","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 : 2022-06-26DOI: 10.1080/07362994.2022.2087677
G. Kumar, M. Mullai
Abstract Introduction This paper discusses the problem of social media addiction that pose a major threat to the human population especially children and teenagers. It is well known that Cognitive Behavioral Therapy (CBT) is an effective treatment to treat the addict individuals and delay in the treatment leads the patient to worst stage even to death. Therefore, it is important to identify the individuals who has addiction symptoms at early stage and to provide proper counseling. Method We propose and analyze a nonlinear mathematical model for social media addiction problem using case detection strategy to reduce the addiction. The basic reproduction number and equilibria of the model are computed. Further, the deterministic model is extended to delay differential equation model by incorporating transmission delay and treatment delay in the system. The local stability of different equilibria is discussed in detail. Additionally, the model is converted to stochastic model and numerical simulation is carried out to compare the results of both deterministic and stochastic model. Results Numerical result shows that the introduction of time delays can destabilize the model system and Hopf bifurcation occurs due to periodic oscillations when certain equilibrium point crosses the delay threshold limit. Our results of stochastic model show a smaller number of social media users and addict population when compared with deterministic model. Also, our results reveal that detection and counseling parameters play a vital role in reducing addiction population. Discussion Presented results clearly suggest that there is a need to use effective detection strategy and suitable counseling program to reduce the social media addiction level.
{"title":"Modeling social media addiction with case detection and treatment","authors":"G. Kumar, M. Mullai","doi":"10.1080/07362994.2022.2087677","DOIUrl":"https://doi.org/10.1080/07362994.2022.2087677","url":null,"abstract":"Abstract Introduction This paper discusses the problem of social media addiction that pose a major threat to the human population especially children and teenagers. It is well known that Cognitive Behavioral Therapy (CBT) is an effective treatment to treat the addict individuals and delay in the treatment leads the patient to worst stage even to death. Therefore, it is important to identify the individuals who has addiction symptoms at early stage and to provide proper counseling. Method We propose and analyze a nonlinear mathematical model for social media addiction problem using case detection strategy to reduce the addiction. The basic reproduction number and equilibria of the model are computed. Further, the deterministic model is extended to delay differential equation model by incorporating transmission delay and treatment delay in the system. The local stability of different equilibria is discussed in detail. Additionally, the model is converted to stochastic model and numerical simulation is carried out to compare the results of both deterministic and stochastic model. Results Numerical result shows that the introduction of time delays can destabilize the model system and Hopf bifurcation occurs due to periodic oscillations when certain equilibrium point crosses the delay threshold limit. Our results of stochastic model show a smaller number of social media users and addict population when compared with deterministic model. Also, our results reveal that detection and counseling parameters play a vital role in reducing addiction population. Discussion Presented results clearly suggest that there is a need to use effective detection strategy and suitable counseling program to reduce the social media addiction level.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42153502","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 : 2022-06-07DOI: 10.1080/07362994.2022.2078839
Ouaddah Abdelhamid, J. Graef, A. Ouahab
Abstract The authors study the existence and uniqueness of solutions to nonlinear first-order fractional stochastic differential systems driven by Brownian motion and with nonlocal functional boundary conditions. The technique of proof involves Perov’s fixed point theorem with matrices that converge to zero and the Leray–Schauder theorem.
{"title":"Existence and uniqueness of solutions of nonlinear fractional stochastic differential systems with nonlocal functional boundary conditions","authors":"Ouaddah Abdelhamid, J. Graef, A. Ouahab","doi":"10.1080/07362994.2022.2078839","DOIUrl":"https://doi.org/10.1080/07362994.2022.2078839","url":null,"abstract":"Abstract The authors study the existence and uniqueness of solutions to nonlinear first-order fractional stochastic differential systems driven by Brownian motion and with nonlocal functional boundary conditions. The technique of proof involves Perov’s fixed point theorem with matrices that converge to zero and the Leray–Schauder theorem.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46691419","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 : 2022-06-02DOI: 10.1080/07362994.2022.2080706
Qiangheng Zhang
Abstract We study the existence, measurability and time-dependent property of pullback random attractors in the higher-order space for stochastic degenerate parabolic equations with variable delay defined on Let X, Z be the square integrable space and the p-times (p > 2) integrable space, respectively. We first prove the existence of a unique pullback -random attractor with and and establish the forward compactness, measurability and long-time stability of the bi-spatial attractor in the higher-order space We then investigate the higher-order delay-free stability of in more precisely, the upper semicontinuity of under the topology of as the memory time tends to zero is established.
{"title":"Higher-order robust attractors for stochastic retarded degenerate parabolic equations","authors":"Qiangheng Zhang","doi":"10.1080/07362994.2022.2080706","DOIUrl":"https://doi.org/10.1080/07362994.2022.2080706","url":null,"abstract":"Abstract We study the existence, measurability and time-dependent property of pullback random attractors in the higher-order space for stochastic degenerate parabolic equations with variable delay defined on Let X, Z be the square integrable space and the p-times (p > 2) integrable space, respectively. We first prove the existence of a unique pullback -random attractor with and and establish the forward compactness, measurability and long-time stability of the bi-spatial attractor in the higher-order space We then investigate the higher-order delay-free stability of in more precisely, the upper semicontinuity of under the topology of as the memory time tends to zero is established.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46913972","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 : 2022-05-30DOI: 10.1080/07362994.2022.2079529
M. Marzougue, M. El Otmani
Abstract We consider reflected backward stochastic differential equations driven by Teugels martingales associated with a Lévy process, in which the barrier process is optional with regulated trajectories (i.e., trajectories with left and right finite limits), which is assumed to be right upper semi-continuous. We prove the existence and uniqueness of such equations by using the predictable representations for Lévy processes due to Nualart and Schoutens, and some tools from the general theory of processes such as Mertens decomposition of optional strong supermartingales. We also discuss the case where the barrier is assumed to be completely irregular, and we establish an infinitesimal characterization of the solution in terms of a value process to an extension of the optimal stopping problem.
{"title":"Irregular barrier reflected BSDEs driven by a Lévy process","authors":"M. Marzougue, M. El Otmani","doi":"10.1080/07362994.2022.2079529","DOIUrl":"https://doi.org/10.1080/07362994.2022.2079529","url":null,"abstract":"Abstract We consider reflected backward stochastic differential equations driven by Teugels martingales associated with a Lévy process, in which the barrier process is optional with regulated trajectories (i.e., trajectories with left and right finite limits), which is assumed to be right upper semi-continuous. We prove the existence and uniqueness of such equations by using the predictable representations for Lévy processes due to Nualart and Schoutens, and some tools from the general theory of processes such as Mertens decomposition of optional strong supermartingales. We also discuss the case where the barrier is assumed to be completely irregular, and we establish an infinitesimal characterization of the solution in terms of a value process to an extension of the optimal stopping problem.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46110448","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：