Pub Date : 2021-05-06DOI: 10.1137/S0040585X97T990289
D. Rokhlin
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 ...
我们考虑一个通信网络，它具有一组由大量用户共享的固定链接。资源分配是在总效用最大化的基础上进行的。
{"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":null,"pages":null},"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}
Pub Date : 2021-05-06DOI: 10.1137/S0040585X97T990290
N. Slepov
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...
本文对Stein方法和随机变量分布变换的辅助技术进行了改进。这使我们能够估计范数分布的收敛速度。
{"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":null,"pages":null},"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}
Pub Date : 2021-05-06DOI: 10.1137/S0040585X97T990265
V. Mosyagin
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...
{"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":null,"pages":null},"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}
Pub Date : 2021-05-06DOI: 10.1137/S0040585X97T990228
G. Afanasyev
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...
{"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":null,"pages":null},"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}
Pub Date : 2021-02-05DOI: 10.1137/S0040585X97T990174
Y. Gliklikh
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...
{"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":null,"pages":null},"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}
Pub Date : 2021-02-05DOI: 10.1137/S0040585X97T990198
Y. Kabanov
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 ...
{"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":null,"pages":null},"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}
Pub Date : 2021-02-05DOI: 10.1137/S0040585X97T990204
V. Konakov, A. Falaleev
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...
{"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":null,"pages":null},"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}
Pub Date : 2021-02-05DOI: 10.1137/S0040585X97T990095
A. Borovkov
The invariance principle for compound renewal processes is extended (in the sense of asymptotic equivalence) to the zone of moderately large and small deviations. It is assumed that the vector $(t...
将复合更新过程的不变性原理（在渐近等价的意义上）推广到中等大小偏差的区域。假设向量$（t。。。
{"title":"Extension of the Invariance Principle for Compound Renewal Processes to the Zones of Moderately Large and Small Deviations","authors":"A. Borovkov","doi":"10.1137/S0040585X97T990095","DOIUrl":"https://doi.org/10.1137/S0040585X97T990095","url":null,"abstract":"The invariance principle for compound renewal processes is extended (in the sense of asymptotic equivalence) to the zone of moderately large and small deviations. It is assumed that the vector $(t...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46728435","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 : 2021-02-05DOI: 10.1137/S0040585X97T990113
A. Gushchin
We consider the family of converging max-continuous local submartingales starting from zero. An equivalence relation for processes of this family is introduced so that two processes are called equi...
{"title":"The Joint Law of a Max-Continuous Local Submartingale and Its Maximum","authors":"A. Gushchin","doi":"10.1137/S0040585X97T990113","DOIUrl":"https://doi.org/10.1137/S0040585X97T990113","url":null,"abstract":"We consider the family of converging max-continuous local submartingales starting from zero. An equivalence relation for processes of this family is introduced so that two processes are called equi...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44069911","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 : 2021-02-05DOI: 10.1137/S0040585X97T990216
M. P. Savelov
We consider the sequential $r$-stage chi-square test. For $r=2$, we study the asymptotic properties of the error probabilities as a function of the sizes of the rectangular critical domain, which v...
{"title":"Two-Stage Chi-Square Test and Two-Dimensional Distributions of a Bessel Process","authors":"M. P. Savelov","doi":"10.1137/S0040585X97T990216","DOIUrl":"https://doi.org/10.1137/S0040585X97T990216","url":null,"abstract":"We consider the sequential $r$-stage chi-square test. For $r=2$, we study the asymptotic properties of the error probabilities as a function of the sizes of the rectangular critical domain, which v...","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46196433","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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