Pub Date : 2021-10-25DOI: 10.1080/07362994.2021.1990082
P. Balasubramaniam
Abstract This paper discusses the existence result for a class of non-instantaneous impulsive Hilfer fractional stochastic systems (NIHFSS) driven by mixed Brownian motion and L vy noise. Sufficient conditions are obtained by utilizing M nch fixed point theorem (FPT) for the existence of solution of non-instantaneous impulsive Hilfer fractional stochastic system of order and of type The existence result is derived by adapting stochastic analysis techniques, the measure of non-compactness, semigroup theory, and fractional calculus. The discussed theory is illustrated through an example.
{"title":"Hilfer fractional stochastic system driven by mixed Brownian motion and L vy noise suffered by non-instantaneous impulses","authors":"P. Balasubramaniam","doi":"10.1080/07362994.2021.1990082","DOIUrl":"https://doi.org/10.1080/07362994.2021.1990082","url":null,"abstract":"Abstract This paper discusses the existence result for a class of non-instantaneous impulsive Hilfer fractional stochastic systems (NIHFSS) driven by mixed Brownian motion and L vy noise. Sufficient conditions are obtained by utilizing M nch fixed point theorem (FPT) for the existence of solution of non-instantaneous impulsive Hilfer fractional stochastic system of order and of type The existence result is derived by adapting stochastic analysis techniques, the measure of non-compactness, semigroup theory, and fractional calculus. The discussed theory is illustrated through an example.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"60 - 79"},"PeriodicalIF":1.3,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45234441","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 : 2021-10-25DOI: 10.1080/07362994.2021.1990778
B. Markovic, M. Nedeljkov
Abstract We consider a symmetric system of conservation laws and its stochastic approximation with stochastic multiplicative noise. Using the vanishing viscosity with the zero-noise limit we obtain a deterministic weak solution for some time interval.
{"title":"A zero-noise limit to a symmetric system of conservation laws","authors":"B. Markovic, M. Nedeljkov","doi":"10.1080/07362994.2021.1990778","DOIUrl":"https://doi.org/10.1080/07362994.2021.1990778","url":null,"abstract":"Abstract We consider a symmetric system of conservation laws and its stochastic approximation with stochastic multiplicative noise. Using the vanishing viscosity with the zero-noise limit we obtain a deterministic weak solution for some time interval.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"102 - 114"},"PeriodicalIF":1.3,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46157892","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 : 2021-10-18DOI: 10.1080/07362994.2021.1989312
T. Caraballo, M. El Fatini, Mohamed El khalifi, A. Rathinasamy
Abstract This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID-19). Severe factors impacting the disease transmission are presented by white noise and compensated Poisson noise with possibly infinite characteristic measure. Large time estimates are established based on Kunita’s inequality rather than Burkholder-Davis-Gundy inequality for continuous diffusions. The effect of stochasticity is taken into account in the formulation of sufficient conditions for the extinction of COVID-19 and its persistence. Our results prove that environmental fluctuations can be privileged in controlling the pandemic behavior. Based on real parameter values, numerical results are presented to illustrate obtained results concerning the extinction and the persistence in mean of the disease.
{"title":"Analysis of a stochastic coronavirus (COVID-19) Lévy jump model with protective measures","authors":"T. Caraballo, M. El Fatini, Mohamed El khalifi, A. Rathinasamy","doi":"10.1080/07362994.2021.1989312","DOIUrl":"https://doi.org/10.1080/07362994.2021.1989312","url":null,"abstract":"Abstract This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID-19). Severe factors impacting the disease transmission are presented by white noise and compensated Poisson noise with possibly infinite characteristic measure. Large time estimates are established based on Kunita’s inequality rather than Burkholder-Davis-Gundy inequality for continuous diffusions. The effect of stochasticity is taken into account in the formulation of sufficient conditions for the extinction of COVID-19 and its persistence. Our results prove that environmental fluctuations can be privileged in controlling the pandemic behavior. Based on real parameter values, numerical results are presented to illustrate obtained results concerning the extinction and the persistence in mean of the disease.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"45 - 59"},"PeriodicalIF":1.3,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48511035","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: 10.1080/07362994.2021.1981383
H. Bessaih, M. Garrido-Atienza, Verena Köpp, B. Schmalfuß
Abstract We consider a system of two coupled stochastic lattice equations driven by additive white noise processes, where the strength of the coupling is given by a parameter We show that these equations generate a random dynamical system which has a random pullback attractor. This attractor naturally depends on the parameter κ. When the intensity of the coupling becomes large, we observe that the components of the given system synchronize. To describe this phenomenon, we prove the upper semicontinuity of the family of attractors with respect to the attractor of a specific limiting system.
{"title":"Synchronization of stochastic lattice equations and upper semicontinuity of attractors","authors":"H. Bessaih, M. Garrido-Atienza, Verena Köpp, B. Schmalfuß","doi":"10.1080/07362994.2021.1981383","DOIUrl":"https://doi.org/10.1080/07362994.2021.1981383","url":null,"abstract":"Abstract We consider a system of two coupled stochastic lattice equations driven by additive white noise processes, where the strength of the coupling is given by a parameter We show that these equations generate a random dynamical system which has a random pullback attractor. This attractor naturally depends on the parameter κ. When the intensity of the coupling becomes large, we observe that the components of the given system synchronize. To describe this phenomenon, we prove the upper semicontinuity of the family of attractors with respect to the attractor of a specific limiting system.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"1067 - 1103"},"PeriodicalIF":1.3,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43931368","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 : 2021-10-10DOI: 10.1080/07362994.2021.1981382
A. El koufi, Jihad Adnani, A. Bennar, N. Yousfi
Abstract In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria E 0 by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results.
{"title":"Dynamics of a stochastic SIR epidemic model driven by Lévy jumps with saturated incidence rate and saturated treatment function","authors":"A. El koufi, Jihad Adnani, A. Bennar, N. Yousfi","doi":"10.1080/07362994.2021.1981382","DOIUrl":"https://doi.org/10.1080/07362994.2021.1981382","url":null,"abstract":"Abstract In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria E 0 by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"1048 - 1066"},"PeriodicalIF":1.3,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45039546","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 : 2021-10-03DOI: 10.1080/07362994.2021.1971539
P. Vellaisamy, Vijay Kumar
Abstract The Adomian decomposition method (ADM) is a powerful tool for solving numerous nonlinear functional equations and a large class of initial/boundary value problems. The main task in the application of ADM is the computation of Adomian polynomials (APs). In addition to classic APs, Rach’s nonclassic APs, called class I-IV polynomials, are used to solve a wide range of nonlinear functional equations. In this paper, we present probabilistic interpretations for the nonclassic APs, including class V polynomials studied by Duan. We derive the recurrence relations for the computation of nonclassic APs using our approach. Some numerical examples are discussed to show that the probabilistic approach to compute the nonclassic APs is attractive and is also simple. Finally, a probabilistic proof is given for the known fact that the class IV APs are the classic APs. The probabilistic approach offers an alternative method to the existing analytical or combinatorial approach.
{"title":"Probabilistic interpretations of nonclassic Adomian polynomials","authors":"P. Vellaisamy, Vijay Kumar","doi":"10.1080/07362994.2021.1971539","DOIUrl":"https://doi.org/10.1080/07362994.2021.1971539","url":null,"abstract":"Abstract The Adomian decomposition method (ADM) is a powerful tool for solving numerous nonlinear functional equations and a large class of initial/boundary value problems. The main task in the application of ADM is the computation of Adomian polynomials (APs). In addition to classic APs, Rach’s nonclassic APs, called class I-IV polynomials, are used to solve a wide range of nonlinear functional equations. In this paper, we present probabilistic interpretations for the nonclassic APs, including class V polynomials studied by Duan. We derive the recurrence relations for the computation of nonclassic APs using our approach. Some numerical examples are discussed to show that the probabilistic approach to compute the nonclassic APs is attractive and is also simple. Finally, a probabilistic proof is given for the known fact that the class IV APs are the classic APs. The probabilistic approach offers an alternative method to the existing analytical or combinatorial approach.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"931 - 950"},"PeriodicalIF":1.3,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47579886","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 : 2021-10-03DOI: 10.1080/07362994.2021.1980014
Qun Liu, D. Jiang
Abstract In this article, a stochastic differential equation model is proposed to investigate how the environmental noise affects the transmission dynamics of the interaction between crime, criminality and victimization with the influence of case reporting through the short message service (SMS). We prove that there is a unique global positive solution of the stochastic system with any positive initial value which is fundamental in the dynamics of population modeling. Moreover, we get sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distribution indicates that both criminal and victim will be persistent and coexistent in the long term.
{"title":"Stationary distribution of a stochastic model for the transmission dynamics of criminality and victimization with migration","authors":"Qun Liu, D. Jiang","doi":"10.1080/07362994.2021.1980014","DOIUrl":"https://doi.org/10.1080/07362994.2021.1980014","url":null,"abstract":"Abstract In this article, a stochastic differential equation model is proposed to investigate how the environmental noise affects the transmission dynamics of the interaction between crime, criminality and victimization with the influence of case reporting through the short message service (SMS). We prove that there is a unique global positive solution of the stochastic system with any positive initial value which is fundamental in the dynamics of population modeling. Moreover, we get sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distribution indicates that both criminal and victim will be persistent and coexistent in the long term.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"996 - 1025"},"PeriodicalIF":1.3,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48847822","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 : 2021-10-03DOI: 10.1080/07362994.2021.1980015
M. Jornet
Abstract Given a random system, a Liouville’s equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive Liouville’s equations for the first-order homogeneous semilinear random partial differential equation. This is done for all finite-dimensional distributions of the random field solution, starting with dimension one, then dimension two, and finally generalizing to any dimension. Several examples, including the linear advection equation with random coefficients, are treated. As a corollary, we deduce Liouville’s equations for path-wise stochastic integrals and nonlinear random ordinary differential equations.
{"title":"Liouville’s equations for random systems","authors":"M. Jornet","doi":"10.1080/07362994.2021.1980015","DOIUrl":"https://doi.org/10.1080/07362994.2021.1980015","url":null,"abstract":"Abstract Given a random system, a Liouville’s equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive Liouville’s equations for the first-order homogeneous semilinear random partial differential equation. This is done for all finite-dimensional distributions of the random field solution, starting with dimension one, then dimension two, and finally generalizing to any dimension. Several examples, including the linear advection equation with random coefficients, are treated. As a corollary, we deduce Liouville’s equations for path-wise stochastic integrals and nonlinear random ordinary differential equations.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"1026 - 1047"},"PeriodicalIF":1.3,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41664502","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 : 2021-09-20DOI: 10.1080/07362994.2022.2120012
Giulia Catalini, B. Pacchiarotti
. We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti [M. Cellupica and B. Pacchiarotti (2021) Pathwise Asymptotics for Volterra Type Stochastic Volatility Models. Journal of Theoretical Probability , 34(2):682–727]. We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles.
{"title":"Asymptotics for multifactor Volterra type stochastic volatility models","authors":"Giulia Catalini, B. Pacchiarotti","doi":"10.1080/07362994.2022.2120012","DOIUrl":"https://doi.org/10.1080/07362994.2022.2120012","url":null,"abstract":". We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti [M. Cellupica and B. Pacchiarotti (2021) Pathwise Asymptotics for Volterra Type Stochastic Volatility Models. Journal of Theoretical Probability , 34(2):682–727]. We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43503551","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: 10.1080/07362994.2021.1970582
Yusen Lin, Dingshi Li
Abstract This paper is concerned with the periodic measures of the stochastic impulsive Hopfield-type lattice systems driven by nonlinear noise. By the properties of periodic Markov processes, the existence of periodic measures for the impulsive stochastic lattice systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.
{"title":"Periodic measures of impulsive stochastic Hopfield-type lattice systems","authors":"Yusen Lin, Dingshi Li","doi":"10.1080/07362994.2021.1970582","DOIUrl":"https://doi.org/10.1080/07362994.2021.1970582","url":null,"abstract":"Abstract This paper is concerned with the periodic measures of the stochastic impulsive Hopfield-type lattice systems driven by nonlinear noise. By the properties of periodic Markov processes, the existence of periodic measures for the impulsive stochastic lattice systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"914 - 930"},"PeriodicalIF":1.3,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47550926","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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