Journal of Theoretical Probability最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"title":"On Markov Intertwining Relations and Primal Conditioning","authors":"Marc Arnaudon, Koléhè Coulibaly-Pasquier, Laurent Miclo","doi":"10.1007/s10959-023-01301-5","DOIUrl":"https://doi.org/10.1007/s10959-023-01301-5","url":null,"abstract":"<p>Given an intertwining relation between two finite Markov chains, we investigate how it can be transformed by conditioning the primal Markov chain to stay in a proper subset. A natural assumption on the underlying link kernel is put forward. The three classical examples of discrete Pitman, top-to-random shuffle and absorbed birth-and-death chain intertwinings serve as illustrations.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"58 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506806","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}

{"title":"Limit Theorem for Self-intersection Local Time Derivative of Multidimensional Fractional Brownian Motion","authors":"Qian Yu, Xianye Yu","doi":"10.1007/s10959-023-01300-6","DOIUrl":"https://doi.org/10.1007/s10959-023-01300-6","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192698","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}

{"title":"A Robust $$alpha $$-Stable Central Limit Theorem Under Sublinear Expectation without Integrability Condition","authors":"Lianzi Jiang, Gechun Liang","doi":"10.1007/s10959-023-01298-x","DOIUrl":"https://doi.org/10.1007/s10959-023-01298-x","url":null,"abstract":"Abstract This article fills a gap in the literature by relaxing the integrability condition for the robust $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> -stable central limit theorem under sublinear expectation. Specifically, for $$alpha in (0,1]$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> , we prove that the normalized sums of i.i.d. non-integrable random variables $$big {n^{-frac{1}{alpha }}sum _{i=1}^{n}Z_{i}big }_{n=1}^{infty }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>{</mml:mo> </mml:mrow> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mi>α</mml:mi> </mml:mfrac> </mml:mrow> </mml:msup> <mml:msubsup> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>n</mml:mi> </mml:msubsup> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:msubsup> <mml:mrow> <mml:mo>}</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> converge in law to $${tilde{zeta }}_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>ζ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> , where $$({tilde{zeta }}_{t})_{tin [0,1]}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mover> <mml:mi>ζ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:msub> </mml:math> is a multidimensional nonlinear symmetric $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> -stable process with jump uncertainty set $${mathcal {L}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>L</mml:mi> </mml:math> . The limiting $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> -stable process is further characterized by a fully nonlinear partial integro-differential equation (PIDE): $$begin{aligned} left{ begin{array}{l} displaystyle partial _{t}u(t,x)-sup limits _{F_{mu }in {mathcal {L}}}left{ int _{{mathbb {R}}^{d}}delta _{lambda }^{alpha }u(t,x)F_{mu }(dlambda )right} =0, displaystyle u(0,x)=phi (x),quad forall (t,x)in [0,1]times {mathbb {R}}^{d}, end{array} right. end{aligned}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mfenced> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:ms","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"39 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818728","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}

{"title":"Shannon–McMillan–Breiman Theorem Along Almost Geodesics in Negatively Curved Groups","authors":"Amos Nevo, Felix Pogorzelski","doi":"10.1007/s10959-023-01291-4","DOIUrl":"https://doi.org/10.1007/s10959-023-01291-4","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"74 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933122","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}

{"title":"Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass","authors":"Luca Avena, Conrado da Costa","doi":"10.1007/s10959-023-01296-z","DOIUrl":"https://doi.org/10.1007/s10959-023-01296-z","url":null,"abstract":"Abstract We consider weighted sums of independent random variables regulated by an increment sequence and provide operative conditions that ensure a strong law of large numbers for such sums in both the centred and non-centred case. The existing criteria for the strong law are either implicit or based on restrictions on the increment sequence. In our setup we allow for an arbitrary sequence of increments, possibly random, provided the random variables regulated by such increments satisfy some mild concentration conditions. In the non-centred case, convergence can be translated into the behaviour of a deterministic sequence and it becomes a game of mass when the expectation of the random variables is a function of the increment sizes. We identify various classes of increments and illustrate them with a variety of concrete examples.","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"225 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018338","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}