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Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena 随机波方程的部分平滑化和噪声现象的正则化
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-20 DOI: 10.1007/s10959-024-01337-1
Federica Masiero, Enrico Priola
{"title":"Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena","authors":"Federica Masiero, Enrico Priola","doi":"10.1007/s10959-024-01337-1","DOIUrl":"https://doi.org/10.1007/s10959-024-01337-1","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141121723","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 Conditioned Local Limit Theorem for Nonnegative Random Matrices 非负随机矩阵的条件局部极限定理
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-13 DOI: 10.1007/s10959-024-01336-2
Marc Peigné, Da Cam Pham
{"title":"A Conditioned Local Limit Theorem for Nonnegative Random Matrices","authors":"Marc Peigné, Da Cam Pham","doi":"10.1007/s10959-024-01336-2","DOIUrl":"https://doi.org/10.1007/s10959-024-01336-2","url":null,"abstract":"<p>For any fixed real <span>(a &gt; 0)</span> and <span>(x in {mathbb {R}}^d, d ge 1)</span>, we consider the real-valued random process <span>((S_n)_{n ge 0})</span> defined by <span>( S_0= a, S_n= a+ln vert g_ncdots g_1xvert , n ge 1)</span>, where the <span>(g_k, k ge 1, )</span> are i.i.d. nonnegative random matrices. By using the strategy initiated by Denisov and Wachtel to control fluctuations in cones of <i>d</i>-dimensional random walks, we obtain an asymptotic estimate and bounds on the probability that the process <span>((S_n)_{n ge 0})</span> remains nonnegative up to time <i>n</i> and simultaneously belongs to some compact set <span>([b, b+ell ]subset {mathbb {R}}^+_*)</span> at time <i>n</i>.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931528","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
Measure Pseudo-S-asymptotically Bloch-Type Periodicity of Some Semilinear Stochastic Integrodifferential Equations 测量某些半线性随机积分微分方程的伪 S-渐近布洛赫型周期性
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-03 DOI: 10.1007/s10959-024-01335-3
Amadou Diop, Mamadou Moustapha Mbaye, Yong-Kui Chang, Gaston Mandata N’Guérékata
{"title":"Measure Pseudo-S-asymptotically Bloch-Type Periodicity of Some Semilinear Stochastic Integrodifferential Equations","authors":"Amadou Diop, Mamadou Moustapha Mbaye, Yong-Kui Chang, Gaston Mandata N’Guérékata","doi":"10.1007/s10959-024-01335-3","DOIUrl":"https://doi.org/10.1007/s10959-024-01335-3","url":null,"abstract":"<p>This paper gives a new property for stochastic processes, called square-mean <span>(mu -)</span>pseudo-<i>S</i>-asymptotically Bloch-type periodicity. We show how this property is preserved under some operations, such as composition and convolution, for stochastic processes. Our main results extend the classical results on S-asymptotically Bloch-type periodic functions. We also apply our results to some problems involving semilinear stochastic integrodifferential equations in abstract spaces</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887391","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
Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators 带对角线发生器的 G 布朗运动驱动的多维反射后向随机微分方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-26 DOI: 10.1007/s10959-024-01334-4
Hanwu Li, Guomin Liu
{"title":"Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators","authors":"Hanwu Li, Guomin Liu","doi":"10.1007/s10959-024-01334-4","DOIUrl":"https://doi.org/10.1007/s10959-024-01334-4","url":null,"abstract":"<p>We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by <i>G</i>-Brownian motion (<i>G</i>-BSDEs) with diagonal generators. Two methods, including the penalization method and the Picard iteration argument, are provided to prove the existence and uniqueness of the solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805674","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
Renewed Limit Theorems for Noncritical Galton–Watson Branching Systems 非临界加尔通-沃森分支系统的更新极限定理
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-24 DOI: 10.1007/s10959-024-01330-8
A. Imomov, Misliddin Murtazaev
{"title":"Renewed Limit Theorems for Noncritical Galton–Watson Branching Systems","authors":"A. Imomov, Misliddin Murtazaev","doi":"10.1007/s10959-024-01330-8","DOIUrl":"https://doi.org/10.1007/s10959-024-01330-8","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140663919","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 the $$L^{p}$$ -Spaces of Projective Limits of Probability Measures 论概率措施的投影极限的 $$L^{p}$$ 空间
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-20 DOI: 10.1007/s10959-024-01329-1
Juan Carlos Sampedro
{"title":"On the $$L^{p}$$ -Spaces of Projective Limits of Probability Measures","authors":"Juan Carlos Sampedro","doi":"10.1007/s10959-024-01329-1","DOIUrl":"https://doi.org/10.1007/s10959-024-01329-1","url":null,"abstract":"<p>The present article describes the precise structure of the <span>(L^{p})</span>-spaces of projective limit measures by introducing a category-theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian measures on nuclear topological vector spaces. A simple application to constructive quantum field theory (QFT) is given through the Osterwalder–Schrader axioms.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140635161","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
Stochastic Differential Equations with Local Growth Singular Drifts 具有局部增长奇异漂移的随机微分方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-19 DOI: 10.1007/s10959-024-01333-5
Wenjie Ye
{"title":"Stochastic Differential Equations with Local Growth Singular Drifts","authors":"Wenjie Ye","doi":"10.1007/s10959-024-01333-5","DOIUrl":"https://doi.org/10.1007/s10959-024-01333-5","url":null,"abstract":"<p>In this paper, we study the weak differentiability of global strong solution of stochastic differential equations, the strong Feller property of the associated diffusion semigroups and the global stochastic flow property in which the singular drift <i>b</i> and the weak gradient of Sobolev diffusion <span>(sigma )</span> are supposed to satisfy <span>(left| left| bright| cdot mathbbm {1}_{B(R)}right| _{p_1}le O((log R)^{{(p_1-d)^2}/{2p^2_1}}))</span> and <span>(left| left| nabla sigma right| cdot mathbbm {1}_{B(R)}right| _{p_1}le O((log ({R}/{3}))^{{(p_1-d)^2}/{2p^2_1}}))</span>, respectively. The main tools for these results are the decomposition of global two-point motions in Fang et al. (Ann Probab 35(1):180–205, 2007), Krylov’s estimate, Khasminskii’s estimate, Zvonkin’s transformation and the characterization for Sobolev differentiability of random fields in Xie and Zhang (Ann Probab 44(6):3661–3687, 2016).\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628807","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
Wigner- and Marchenko–Pastur-Type Limit Theorems for Jacobi Processes 雅可比过程的维格纳和马琴科-帕斯图尔型极限定理
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-11 DOI: 10.1007/s10959-024-01332-6
Martin Auer, Michael Voit, Jeannette H. C. Woerner
{"title":"Wigner- and Marchenko–Pastur-Type Limit Theorems for Jacobi Processes","authors":"Martin Auer, Michael Voit, Jeannette H. C. Woerner","doi":"10.1007/s10959-024-01332-6","DOIUrl":"https://doi.org/10.1007/s10959-024-01332-6","url":null,"abstract":"<p>We study Jacobi processes <span>((X_{t})_{tge 0})</span> on <span>([-1,1]^N)</span> and <span>([1,infty [^N)</span> which are motivated by the Heckman–Opdam theory and associated integrable particle systems. These processes depend on three positive parameters and degenerate in the freezing limit to solutions of deterministic dynamical systems. In the compact case, these models tend for <span>(trightarrow infty )</span> to the distributions of the <span>(beta )</span>-Jacobi ensembles and, in the freezing case, to vectors consisting of ordered zeros of one-dimensional Jacobi polynomials. We derive almost sure analogues of Wigner’s semicircle and Marchenko–Pastur limit laws for <span>(Nrightarrow infty )</span> for the empirical distributions of the <i>N</i> particles on some local scale. We there allow for arbitrary initial conditions, which enter the limiting distributions via free convolutions. These results generalize corresponding stationary limit results in the compact case for <span>(beta )</span>-Jacobi ensembles and, in the deterministic case, for the empirical distributions of the ordered zeros of Jacobi polynomials. The results are also related to free limit theorems for multivariate Bessel processes, <span>(beta )</span>-Hermite and <span>(beta )</span>-Laguerre ensembles, and the asymptotic empirical distributions of the zeros of Hermite and Laguerre polynomials for <span>(Nrightarrow infty )</span>.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561698","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
Reflected and Doubly Reflected Backward Stochastic Differential Equations with Irregular Obstacles and a Large Set of Stopping Strategies 具有不规则障碍和大量停止策略的反射和双重反射后向随机微分方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-11 DOI: 10.1007/s10959-024-01331-7
Ihsan Arharas, Youssef Ouknine
{"title":"Reflected and Doubly Reflected Backward Stochastic Differential Equations with Irregular Obstacles and a Large Set of Stopping Strategies","authors":"Ihsan Arharas, Youssef Ouknine","doi":"10.1007/s10959-024-01331-7","DOIUrl":"https://doi.org/10.1007/s10959-024-01331-7","url":null,"abstract":"<p>We introduce a new formulation of reflected backward stochastic differential equations (BSDEs) and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of stopping systems than the set of stopping times (namely, the set of <i>split stopping times</i>), where the payoff process <span>(xi )</span> is irregular and in the case of a general filtration. Split stopping times are a powerful tool for modeling financial contracts and derivatives that depend on multiple conditions or triggers, and for incorporating stochastic processes with jumps and other types of discontinuities. We show that the value family can be aggregated by an optional process <i>v</i>, which is characterized as the Snell envelope of the reward process <span>(xi )</span> over split stopping times. Using this, we prove the existence and uniqueness of a solution <i>Y</i> to irregular reflected BSDEs. In the second part of the paper, motivated by the classical Dynkin game with completely irregular rewards considered by Grigorova et al. (Electron J Probab 23:1–38, 2018), we generalize the previous equations to the case of two reflecting barrier processes.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561707","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
Stochastic Differential Equations with Singular Coefficients: The Martingale Problem View and the Stochastic Dynamics View 具有奇异系数的随机微分方程：马丁格尔问题观点和随机动力学观点
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-06 DOI: 10.1007/s10959-024-01325-5
Elena Issoglio, Francesco Russo
{"title":"Stochastic Differential Equations with Singular Coefficients: The Martingale Problem View and the Stochastic Dynamics View","authors":"Elena Issoglio, Francesco Russo","doi":"10.1007/s10959-024-01325-5","DOIUrl":"https://doi.org/10.1007/s10959-024-01325-5","url":null,"abstract":"<p>We consider stochastic differential equations (SDEs) with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness. We then prove further properties of the martingale problem, such as continuity with respect to the drift and the link with the Fokker–Planck equation. We also show that the solutions are weak Dirichlet processes for which we evaluate the quadratic variation of the martingale component. In the second part we identify the dynamics of the solution of the martingale problem by describing the proper associated SDE. Under suitable assumptions we show equivalence with the solution to the martingale problem.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561691","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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