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Waiting Time for a Small Subcollection in the Coupon Collector Problem with Universal Coupon 带通用优惠券的优惠券收集器问题中小规模子收集的等待时间
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-01-21 DOI: 10.1007/s10959-023-01312-2
Jelena Jocković, Bojana Todić
{"title":"Waiting Time for a Small Subcollection in the Coupon Collector Problem with Universal Coupon","authors":"Jelena Jocković, Bojana Todić","doi":"10.1007/s10959-023-01312-2","DOIUrl":"https://doi.org/10.1007/s10959-023-01312-2","url":null,"abstract":"<p>We consider a generalization of the classical coupon collector problem, where the set of available coupons consists of standard coupons (which can be part of the collection), and two coupons with special purposes: one that speeds up the collection process and one that slows it down. We obtain several asymptotic results related to the expectation and the variance of the waiting time until a portion of the collection is sampled, as the number of standard coupons tends to infinity.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139517463","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
A Note on Transience of Generalized Multi-Dimensional Excited Random Walks 广义多维受激随机漫步的瞬态说明
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-01-11 DOI: 10.1007/s10959-023-01311-3
Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle
{"title":"A Note on Transience of Generalized Multi-Dimensional Excited Random Walks","authors":"Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle","doi":"10.1007/s10959-023-01311-3","DOIUrl":"https://doi.org/10.1007/s10959-023-01311-3","url":null,"abstract":"<p>We consider a variant of the generalized excited random walk (GERW) in dimension <span>(dge 2)</span> where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays more slowly than <span>(n^{-beta _0})</span> (<i>n</i> is time), where <span>(beta _0)</span> depends on the transitions of the process, the GERW is transient in the direction of the drift.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"54 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139460832","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 Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${textbf{F}}_psi (Omega )$$ 论来自 $${textbf{F}}_psi (Omega )$$ 空间的随机过程的统一规范和逼近的收敛性
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-12-20 DOI: 10.1007/s10959-023-01309-x
Iryna Rozora, Yurii Mlavets, Olga Vasylyk, Volodymyr Polishchuk
{"title":"On Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${textbf{F}}_psi (Omega )$$","authors":"Iryna Rozora, Yurii Mlavets, Olga Vasylyk, Volodymyr Polishchuk","doi":"10.1007/s10959-023-01309-x","DOIUrl":"https://doi.org/10.1007/s10959-023-01309-x","url":null,"abstract":"<p>In this paper, we consider random variables and stochastic processes from the space <span>({textbf{F}}_psi (Omega ))</span> and study approximation problems for such processes. The method of series decomposition of a stochastic process from <span>({textbf{F}}_psi (Omega ))</span> is used to find an approximating process called a model. The rate of convergence of the model to the process in the uniform norm is investigated. We develop an approach for estimating the cut-off level of the model under given accuracy and reliability of the simulation.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138820069","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
The Time-Dependent Symbol of a Non-homogeneous Itô Process and Corresponding Maximal Inequalities 非均质伊托过程的时变符号及相应的最大不等式
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-12-19 DOI: 10.1007/s10959-023-01308-y
{"title":"The Time-Dependent Symbol of a Non-homogeneous Itô Process and Corresponding Maximal Inequalities","authors":"","doi":"10.1007/s10959-023-01308-y","DOIUrl":"https://doi.org/10.1007/s10959-023-01308-y","url":null,"abstract":"<h3>Abstract</h3> <p>The probabilistic symbol is defined as the right-hand side derivative at time zero of the characteristic functions corresponding to the one-dimensional marginals of a time-homogeneous stochastic process. As described in various contributions to this topic, the symbol contains crucial information concerning the process. When leaving time-homogeneity behind, a modification of the symbol by inserting a time component is needed. In the present article, we show the existence of such a time-dependent symbol for non-homogeneous Itô processes. Moreover, for this class of processes, we derive maximal inequalities which we apply to generalize the Blumenthal–Getoor indices to the non-homogeneous case. These are utilized to derive several properties regarding the paths of the process, including the asymptotic behavior of the sample paths, the existence of exponential moments and the finiteness of <em>p</em>-variationa. In contrast to many situations where non-homogeneous Markov processes are involved, the space-time process <em>cannot</em> be utilized when considering maximal inequalities.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"215 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138741372","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
The Moduli of Continuity for Operator Fractional Brownian Motion 算子分数布朗运动的连续性模量
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-12-15 DOI: 10.1007/s10959-023-01307-z
Wensheng Wang
{"title":"The Moduli of Continuity for Operator Fractional Brownian Motion","authors":"Wensheng Wang","doi":"10.1007/s10959-023-01307-z","DOIUrl":"https://doi.org/10.1007/s10959-023-01307-z","url":null,"abstract":"<p>The almost-sure sample path behavior of the operator fractional Brownian motion with exponent <i>D</i>, including multivariate fractional Brownian motion, is investigated. In particular, the global and the local moduli of continuity of the sample paths are established. These results show that the global and the local moduli of continuity of the sample paths are completely determined by the real parts of the eigenvalues of the exponent <i>D</i>, as well as the covariance matrix at some unit vector. These results are applicable to multivariate fractional Brownian motion.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"190 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138689353","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
Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails 一类具有半指数尾的相关随机变量的强逼近
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-12-06 DOI: 10.1007/s10959-023-01306-0
Christophe Cuny, Jérôme Dedecker, Florence Merlevède
{"title":"Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails","authors":"Christophe Cuny, Jérôme Dedecker, Florence Merlevède","doi":"10.1007/s10959-023-01306-0","DOIUrl":"https://doi.org/10.1007/s10959-023-01306-0","url":null,"abstract":"<p>We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi-exponential tails, whose coupling coefficients decrease at a sub-exponential rate. We show that the rates in the strong invariance principle are in powers of <span>(log n)</span>. We apply our results to iid products of random matrices.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"55 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506808","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
Sojourn Times of Gaussian Processes with Random Parameters 随机参数高斯过程的逗留时间
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-11-25 DOI: 10.1007/s10959-023-01305-1
Goran Popivoda, Siniša Stamatović
{"title":"Sojourn Times of Gaussian Processes with Random Parameters","authors":"Goran Popivoda, Siniša Stamatović","doi":"10.1007/s10959-023-01305-1","DOIUrl":"https://doi.org/10.1007/s10959-023-01305-1","url":null,"abstract":"<p>In this paper, we investigate the sojourn times of conditionally Gaussian processes, i.e., the sojourns of <span>(xi (t)+lambda -zeta ,t^beta )</span> and <span>(xi (t)(lambda -zeta ,t^beta ))</span>, <span>(tin [0, T], T&gt;0)</span>, where <span>(xi )</span> is a Gaussian zero-mean stationary process and <span>(lambda )</span> and <span>(zeta )</span> are random variables independent of <span>(xi (cdot ))</span>, and <span>(beta &gt;0)</span> is a constant.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506803","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
Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms 一类具有空间依赖分支机构的超布朗运动的极限分布
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-11-25 DOI: 10.1007/s10959-023-01304-2
Yan-Xia Ren, Ting Yang
{"title":"Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms","authors":"Yan-Xia Ren, Ting Yang","doi":"10.1007/s10959-023-01304-2","DOIUrl":"https://doi.org/10.1007/s10959-023-01304-2","url":null,"abstract":"<p>In this paper, we consider a large class of super-Brownian motions in <span>({mathbb {R}})</span> with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mass located outside a time-dependent interval <span>((-delta t,delta t))</span> for <span>(delta &gt;0)</span>. The growth rate is given in terms of the principal eigenvalue <span>(lambda _{1})</span> of the Schrödinger-type operator associated with the branching mechanism. From this result, we see the existence of phase transition for the growth order at <span>(delta =sqrt{lambda _{1}/2})</span>. We further show that the super-Brownian motion shifted by <span>(sqrt{lambda _{1}/2},t)</span> converges in distribution to a random measure with random density mixed by a martingale limit.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"58 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506805","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
Coupled McKean–Vlasov Equations Over Convex Domains 凸域上的耦合McKean-Vlasov方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-11-18 DOI: 10.1007/s10959-023-01303-3
Guangying Lv, Wei Wang, Jinlong Wei
{"title":"Coupled McKean–Vlasov Equations Over Convex Domains","authors":"Guangying Lv, Wei Wang, Jinlong Wei","doi":"10.1007/s10959-023-01303-3","DOIUrl":"https://doi.org/10.1007/s10959-023-01303-3","url":null,"abstract":"<p>In this paper, the reflected McKean–Vlasov diffusion ov a convex domain is studied. We first establish the well-posedness of a coupled system of nonlinear stochastic differential equations via a fixed point theorem which is similar to that for partial differential equations. Moreover, the reason why we make different assumptions on drift and cross terms is given. Then, the propagation of chaos for the particle system is also obtained.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"58 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506807","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
Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States 具有瞬时态的可数马尔可夫过程的存在唯一性
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-11-18 DOI: 10.1007/s10959-023-01299-w
Xiaohan Wu, Anyue Chen, Junping Li
{"title":"Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States","authors":"Xiaohan Wu, Anyue Chen, Junping Li","doi":"10.1007/s10959-023-01299-w","DOIUrl":"https://doi.org/10.1007/s10959-023-01299-w","url":null,"abstract":"<p>Based on the resolvent decomposition theorems presented very recently by Chen (J Theor Probab 33:2089–2118, 2020), in this paper we focus on investigating the fundamental problems of existence and uniqueness criteria for Denumerable Markov Processes with finitely many instantaneous states. Some elegant sufficient and necessary conditions are obtained for this less-investigated topic. A few important examples including the generalized Kolmogorov models are presented to illustrate our general results.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543381","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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