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An Estimate for the Sum of the Spitzer Series and Its Generalization Spitzer级数和的一个估计及其推广
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990277
S. Nagaev
{"title":"An Estimate for the Sum of the Spitzer Series and Its Generalization","authors":"S. Nagaev","doi":"10.1137/S0040585X97T990277","DOIUrl":"https://doi.org/10.1137/S0040585X97T990277","url":null,"abstract":"An upper estimate for the absolute value of the sum of the Spitzer series is obtained. This estimate depends explicitly on the distribution in terms of which the Spitzer series is defined.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"89-104"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46812612","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}
引用次数: 0
Systems of Nonlinear Backward and Forward Kolmogorov Equations: Generalized Solutions 非线性后向和正向Kolmogorov方程系统:广义解
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T99023X
Y. Belopolskaya
{"title":"Systems of Nonlinear Backward and Forward Kolmogorov Equations: Generalized Solutions","authors":"Y. Belopolskaya","doi":"10.1137/S0040585X97T99023X","DOIUrl":"https://doi.org/10.1137/S0040585X97T99023X","url":null,"abstract":"A probabilistic approach to construction of the solution to the Cauchy problem for systems of nonlinear parabolic equations is developed. The systems under consideration can be subdivided into two ...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"15-43"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46845600","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}
引用次数: 0
Conditional Quantile Reproducibility of Multivariate Distributions and Simplified Pair Copula Construction 多元分布的条件分位数再现性和简化的对Copula构造
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990319
L. E. Melkumova, S. Y. Shatskikh
{"title":"Conditional Quantile Reproducibility of Multivariate Distributions and Simplified Pair Copula Construction","authors":"L. E. Melkumova, S. Y. Shatskikh","doi":"10.1137/S0040585X97T990319","DOIUrl":"https://doi.org/10.1137/S0040585X97T990319","url":null,"abstract":"We give an equivalent definition of the conditional quantile reproducibility property for multivariate probability distributions using the concept of copula. Based on this definition, we establish ...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"160-168"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44711691","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}
引用次数: 0
Resource Allocation in Communication Networks with Large Number of Users: The Dual Stochastic Gradient Method 大用户通信网络中的资源分配:双随机梯度法
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990289
D. Rokhlin
{"title":"Resource Allocation in Communication Networks with Large Number of Users: The Dual Stochastic Gradient Method","authors":"D. Rokhlin","doi":"10.1137/S0040585X97T990289","DOIUrl":"https://doi.org/10.1137/S0040585X97T990289","url":null,"abstract":"We consider a communication network with a fixed set of links that are shared by a large number of users. The resource allocation is performed on the basis of the aggregate utility maximization in ...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"105-120"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44401131","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}
引用次数: 2
Convergence Rate of Random Geometric Sum Distributions to the Laplace Law 随机几何和分布对拉普拉斯定律的收敛速度
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990290
N. Slepov
{"title":"Convergence Rate of Random Geometric Sum Distributions to the Laplace Law","authors":"N. Slepov","doi":"10.1137/S0040585X97T990290","DOIUrl":"https://doi.org/10.1137/S0040585X97T990290","url":null,"abstract":"In this paper we modify the Stein method and the auxiliary technique of distributional transformations of random variables. This enables us to estimate the convergence rate of distributions of norm...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"121-141"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48318775","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}
引用次数: 5
A Vacation Queue $M|G|1$ with Close-Down Times 带关闭时间的休假队列$M b| G b| 1$
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990228
G. Afanasyev
{"title":"A Vacation Queue $M|G|1$ with Close-Down Times","authors":"G. Afanasyev","doi":"10.1137/S0040585X97T990228","DOIUrl":"https://doi.org/10.1137/S0040585X97T990228","url":null,"abstract":"We consider a single-channel system with service vacations, a Poisson input flow, and an arbitrarily distributed service time. Interruptions in service can mean either a complete shutdown of the se...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"1-14"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44940368","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}
引用次数: 0
Asymptotics for the Distribution of the Time of Attaining the Maximum for a Trajectory of a Poisson Process with Linear Drift and Intensity Switch 具有线性漂移和强度切换的泊松过程轨迹达到最大值时间分布的渐近性
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-05-06 DOI: 10.1137/S0040585X97T990265
V. Mosyagin
{"title":"Asymptotics for the Distribution of the Time of Attaining the Maximum for a Trajectory of a Poisson Process with Linear Drift and Intensity Switch","authors":"V. Mosyagin","doi":"10.1137/S0040585X97T990265","DOIUrl":"https://doi.org/10.1137/S0040585X97T990265","url":null,"abstract":"We find the exact asymptotics of the distribution of the time when the trajectory of the process $Y(t)=at-nu_+(pt)+nu_-(-qt)$, $tin(-infty,infty)$ attains its maximum, where $nu_{pm}(t)$ are...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"66 1","pages":"75-88"},"PeriodicalIF":0.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45558407","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}
引用次数: 0
On Solvability of Stochastic Differential Equations with Osmotic Velocities 具有渗透速度的随机微分方程的可解性
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-02-05 DOI: 10.1137/S0040585X97T990174
Y. Gliklikh
{"title":"On Solvability of Stochastic Differential Equations with Osmotic Velocities","authors":"Y. Gliklikh","doi":"10.1137/S0040585X97T990174","DOIUrl":"https://doi.org/10.1137/S0040585X97T990174","url":null,"abstract":"We give conditions such that solutions exist of the stochastic equation with the so-called osmotic velocities (the so-called Nelson's antisymmetric mean derivatives). We show that the solutions may...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"65 1","pages":"640-647"},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42189098","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}
引用次数: 1
On Sets of Laws of Continuous Martingales 关于连续鞅定律的集合
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-02-05 DOI: 10.1137/S0040585X97T990198
Y. Kabanov
{"title":"On Sets of Laws of Continuous Martingales","authors":"Y. Kabanov","doi":"10.1137/S0040585X97T990198","DOIUrl":"https://doi.org/10.1137/S0040585X97T990198","url":null,"abstract":"We prove that the set of laws of stochastic integrals $H,{cdot}, W$, where $W$ is a multidimensional Wiener process and $H^2$ takes values in a compact convex subset $D$ of the set of symmetric ...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"65 1","pages":"652-655"},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45127643","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}
引用次数: 0
Convergence of Certain Classes of Random Flights in the Kantorovich Metric Kantorovich度量中若干类随机飞行的收敛性
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2021-02-05 DOI: 10.1137/S0040585X97T990204
V. Konakov, A. Falaleev
{"title":"Convergence of Certain Classes of Random Flights in the Kantorovich Metric","authors":"V. Konakov, A. Falaleev","doi":"10.1137/S0040585X97T990204","DOIUrl":"https://doi.org/10.1137/S0040585X97T990204","url":null,"abstract":"A random walk of a particle in ${R}^d$ is considered. The weak convergence of various transformations of trajectories of random flights with Poisson switching times was studied by Davydov and Konak...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"65 1","pages":"656-664"},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49532514","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}
引用次数: 0
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