Pub Date : 2023-02-10DOI: 10.1142/s0219493723500223
J. Villarroel, J. A. Vega
{"title":"The two barrier escape problem for compound renewal processes with two-sided jumps","authors":"J. Villarroel, J. A. Vega","doi":"10.1142/s0219493723500223","DOIUrl":"https://doi.org/10.1142/s0219493723500223","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48851626","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 : 2023-02-10DOI: 10.1142/s0219493723500247
Xuekang Zhang
{"title":"Asymptotic behaviour of maximum likelihood estimators for Ornstein-Uhlenbeck process with large linear drift","authors":"Xuekang Zhang","doi":"10.1142/s0219493723500247","DOIUrl":"https://doi.org/10.1142/s0219493723500247","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46599329","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 : 2023-02-03DOI: 10.1142/s0219493722400330
Hongyan Ma, Hongjun Gao
In this paper, we consider a class of rough nonlinear evolution equations driven by infinite-dimensional -Hölder rough paths with . First, we give a proper integral with respect to infinite-dimensional -Hölder rough paths by using rough paths theory. Second, we obtain the global in time solution and random dynamical system of rough evolution equation. Finally, we derive the existence of local unstable manifolds for rough evolution equations by a properly discretized Lyapunov–Perron method.
{"title":"Unstable manifolds for rough evolution equations","authors":"Hongyan Ma, Hongjun Gao","doi":"10.1142/s0219493722400330","DOIUrl":"https://doi.org/10.1142/s0219493722400330","url":null,"abstract":"<p>In this paper, we consider a class of rough nonlinear evolution equations driven by infinite-dimensional <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>γ</mi></math></span><span></span>-Hölder rough paths with <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>γ </mi><mi>∈ </mi><mo stretchy=\"false\">(</mo><mn>1</mn><mo stretchy=\"false\">/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">/</mo><mn>2</mn><mo stretchy=\"false\">]</mo></math></span><span></span>. First, we give a proper integral with respect to infinite-dimensional <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>γ</mi></math></span><span></span>-Hölder rough paths by using rough paths theory. Second, we obtain the global in time solution and random dynamical system of rough evolution equation. Finally, we derive the existence of local unstable manifolds for rough evolution equations by a properly discretized Lyapunov–Perron method.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":"253 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507998","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 : 2023-01-26DOI: 10.1142/s021949372202004x
Hongjun Gao, B. Schmalfuß, Wen Wang
{"title":"Special issue: Random dynamics","authors":"Hongjun Gao, B. Schmalfuß, Wen Wang","doi":"10.1142/s021949372202004x","DOIUrl":"https://doi.org/10.1142/s021949372202004x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":"76 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41246776","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 : 2023-01-12DOI: 10.1142/s0219493723500156
Jinying Tong, Ruifang Wu, Qianqian Zhang, Zhenzhong Zhang, E. Zhu
In this paper, we consider some properties of switching Brownian motion. Combining the analytic method and probabilistic method, some explicit expressions of density functions, the mean exit time and Laplace transform of exit time are given. This paper reveals how drift coefficients impact the first passage probabilities, scale functions and the mean exit time for switching Brownian motion.
{"title":"First passage time and mean exit time for switching Brownian motion","authors":"Jinying Tong, Ruifang Wu, Qianqian Zhang, Zhenzhong Zhang, E. Zhu","doi":"10.1142/s0219493723500156","DOIUrl":"https://doi.org/10.1142/s0219493723500156","url":null,"abstract":"In this paper, we consider some properties of switching Brownian motion. Combining the analytic method and probabilistic method, some explicit expressions of density functions, the mean exit time and Laplace transform of exit time are given. This paper reveals how drift coefficients impact the first passage probabilities, scale functions and the mean exit time for switching Brownian motion.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41968076","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 : 2023-01-06DOI: 10.1142/s0219493722400391
Anirban Das, M. Denker, Anna Levina, Lucia Tabacu
{"title":"A Monte Carlo algorithm for multiple stochastic integrals of stable processes","authors":"Anirban Das, M. Denker, Anna Levina, Lucia Tabacu","doi":"10.1142/s0219493722400391","DOIUrl":"https://doi.org/10.1142/s0219493722400391","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44205007","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 : 2022-12-30DOI: 10.1142/s021949372350020x
J. Newman, P. Ashwin
{"title":"Physical measures of asymptotically autonomous dynamical systems","authors":"J. Newman, P. Ashwin","doi":"10.1142/s021949372350020x","DOIUrl":"https://doi.org/10.1142/s021949372350020x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47178264","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 : 2022-12-30DOI: 10.1142/s0219493723500193
Jiangwei Zhang, Zhiming Liu, Jianhua Huang
{"title":"Weak mean random attractors for nonautonomous stochastic parabolic equation with variable exponents","authors":"Jiangwei Zhang, Zhiming Liu, Jianhua Huang","doi":"10.1142/s0219493723500193","DOIUrl":"https://doi.org/10.1142/s0219493723500193","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42174314","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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