Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990575
A. Shiryaev
{"title":"On the Bicentenary of the Birth of P. L. Chebyshev, A Great Russian Mathematician","authors":"A. Shiryaev","doi":"10.1137/s0040585x97t990575","DOIUrl":"https://doi.org/10.1137/s0040585x97t990575","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87399043","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 : 2022-02-01DOI: 10.1137/s0040585x97t990629
A. Borovkov, A. Logachov, A. Mogulskii
{"title":"Chebyshev-Type Inequalities and Large Deviation Principles","authors":"A. Borovkov, A. Logachov, A. Mogulskii","doi":"10.1137/s0040585x97t990629","DOIUrl":"https://doi.org/10.1137/s0040585x97t990629","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85838890","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 : 2022-02-01DOI: 10.1137/s0040585x97t990691
N. Kordzakhia, A. Novikov
{"title":"On Maximal Inequalities for Ornstein--Uhlenbeck Processes with Jumps","authors":"N. Kordzakhia, A. Novikov","doi":"10.1137/s0040585x97t990691","DOIUrl":"https://doi.org/10.1137/s0040585x97t990691","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"55 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86316498","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: 10.1137/S0040585X97979524
S. Kuksin, N. Nadirashvili, Andrey L. Piatnitski
This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of~${bf R}^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large~p. We prove that the solutions are H"older-continuous functions almost surely (a.s.) and that the respective H"older norms have finite momenta of any order.
{"title":"Holder Estimates for Solutions of Parabolic SPDEs","authors":"S. Kuksin, N. Nadirashvili, Andrey L. Piatnitski","doi":"10.1137/S0040585X97979524","DOIUrl":"https://doi.org/10.1137/S0040585X97979524","url":null,"abstract":"This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of~${bf R}^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large~p. We prove that the solutions are H\"older-continuous functions almost surely (a.s.) and that the respective H\"older norms have finite momenta of any order.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"47 1","pages":"157-163"},"PeriodicalIF":0.6,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/S0040585X97979524","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41328632","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 : 2021-09-10DOI: 10.1137/s0040585x97t990630
E. Feinberg, A. Shiryaev
This paper describes the structure of solutions to Kolmogorov’s equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic systems. These equations were studied by Feller (1940), who clarified in 1945 in the errata to that paper that some of its results covered only nonexplosive Markov processes. In this work, which is largely of a survey nature, the case of explosive processes is also considered. This paper is based on the invited talk presented by the authors at the conference “Chebyshev-200”, and it describes the results of their joined studies with Manasa Mandava (1984-2019).
{"title":"Kolmogorov's Equations for Jump Markov Processes and Their Applications to Control Problems","authors":"E. Feinberg, A. Shiryaev","doi":"10.1137/s0040585x97t990630","DOIUrl":"https://doi.org/10.1137/s0040585x97t990630","url":null,"abstract":"This paper describes the structure of solutions to Kolmogorov’s equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic systems. These equations were studied by Feller (1940), who clarified in 1945 in the errata to that paper that some of its results covered only nonexplosive Markov processes. In this work, which is largely of a survey nature, the case of explosive processes is also considered. This paper is based on the invited talk presented by the authors at the conference “Chebyshev-200”, and it describes the results of their joined studies with Manasa Mandava (1984-2019).","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88426147","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 : 2021-08-05DOI: 10.1137/s0040585x97t990368
V. Zadorozhniy
We consider a linear inhomogeneous system of differential equations of special form with three random coefficients defined by characteristic functionals. Operator functions generated by the functio...
考虑一类具有特征泛函定义的三个随机系数的特殊形式线性非齐次微分方程系统。操作符函数由函数…
{"title":"The Expectation of a Solution of a Linear System of Differential Equations with Random Coefficients","authors":"V. Zadorozhniy","doi":"10.1137/s0040585x97t990368","DOIUrl":"https://doi.org/10.1137/s0040585x97t990368","url":null,"abstract":"We consider a linear inhomogeneous system of differential equations of special form with three random coefficients defined by characteristic functionals. Operator functions generated by the functio...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"82 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76132459","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 : 2021-08-05DOI: 10.1137/s0040585x97t990344
F. Aurzada, V. Betz, M. Lifshits
We investigate the behavior of a finite chain of Brownian particles interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, ...
我们研究了一个有限的布朗粒子链通过一对二次势相互作用的行为，链的一端固定，另一端以缓慢的速度拉开。
{"title":"Breaking a Chain of Interacting Brownian Particles: A Gumbel Limit Theorem","authors":"F. Aurzada, V. Betz, M. Lifshits","doi":"10.1137/s0040585x97t990344","DOIUrl":"https://doi.org/10.1137/s0040585x97t990344","url":null,"abstract":"We investigate the behavior of a finite chain of Brownian particles interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, ...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86895092","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 : 2021-08-05DOI: 10.1137/s0040585x97t990411
A. I. Rubinshtein, V. Sherstyukov
Extensions of S.N. Bernstein's example of three dependent random events of which any two are independent are considered. A complete description of such examples is given in the framework of the sym...
{"title":"On a Probabilistic Bernstein Model","authors":"A. I. Rubinshtein, V. Sherstyukov","doi":"10.1137/s0040585x97t990411","DOIUrl":"https://doi.org/10.1137/s0040585x97t990411","url":null,"abstract":"Extensions of S.N. Bernstein's example of three dependent random events of which any two are independent are considered. A complete description of such examples is given in the framework of the sym...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"69 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85689399","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 : 2021-08-05DOI: 10.1137/s0040585x97t990356
G. A. Bakay
Let $(xi(i),eta(i)) in {R}^{d+1}$, $i in {N}$, be independent and identically distributed random vectors, let $xi(i)in {R}^d$ be random vectors, let $eta(i)$ be improper nonnegative random v...
设$(xi(i)，eta(i)) in {R}^{d+1}$， $i in {N}$是独立的同分布随机向量，设$xi(i)in {R}^d$是随机向量，设$eta(i)$是反常的非负随机v…
{"title":"Large Deviations for a Terminating Compound Renewal Process","authors":"G. A. Bakay","doi":"10.1137/s0040585x97t990356","DOIUrl":"https://doi.org/10.1137/s0040585x97t990356","url":null,"abstract":"Let $(xi(i),eta(i)) in {R}^{d+1}$, $i in {N}$, be independent and identically distributed random vectors, let $xi(i)in {R}^d$ be random vectors, let $eta(i)$ be improper nonnegative random v...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88697989","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 : 2021-08-05DOI: 10.1137/s0040585x97t990332
A. Borovkov
We consider two large deviation principles (LDPs): the “ordinary” LDP (when the “strong” Cramer condition is met) and the “extended” LDP when only the standard Cramer condition is met and the devia...
{"title":"On Exact Large Deviation Principles for Compound Renewal Processes","authors":"A. Borovkov","doi":"10.1137/s0040585x97t990332","DOIUrl":"https://doi.org/10.1137/s0040585x97t990332","url":null,"abstract":"We consider two large deviation principles (LDPs): the “ordinary” LDP (when the “strong” Cramer condition is met) and the “extended” LDP when only the standard Cramer condition is met and the devia...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81080684","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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