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Least squares type estimators for the drift parameters in the sub-bifractional Vasicek processes 子分分数Vasicek过程漂移参数的最小二乘估计
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-03-10 DOI: 10.1142/s0219025723500042
Nenghui Kuang, Huantian Xie
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引用次数: 1
The stockwell transform on locally compact abelian groups 局部紧阿贝尔群上的stockwell变换
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-03-10 DOI: 10.1142/s0219025723500029
F. Esmaeelzadeh
{"title":"The stockwell transform on locally compact abelian groups","authors":"F. Esmaeelzadeh","doi":"10.1142/s0219025723500029","DOIUrl":"https://doi.org/10.1142/s0219025723500029","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73971388","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
Algebraic central limit theorems: A personal view on one of Wilhelm’s legacies 代数中心极限定理:威廉的一个个人观点
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-31 DOI: 10.1142/s0219025722400033
Michael Skeide
{"title":"Algebraic central limit theorems: A personal view on one of Wilhelm’s legacies","authors":"Michael Skeide","doi":"10.1142/s0219025722400033","DOIUrl":"https://doi.org/10.1142/s0219025722400033","url":null,"abstract":"<p>Bringing forward the concept of convergence in moments from classical random variables to quantum random variables leads to what can be called algebraic central limit theorem for (classical and) quantum random variables. I reflect in a very personal way how such an idea is typical for the spirit of doing research in mathematics as I learned it in Wilhelm von Waldenfels’s research group in Heidelberg.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514077","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 Quantization of Laser Propagation Models 激光传播模型的随机量化
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-31 DOI: 10.1142/s0219025723500108
S. Sritharan, S. Mudaliar
{"title":"Stochastic Quantization of Laser Propagation Models","authors":"S. Sritharan, S. Mudaliar","doi":"10.1142/s0219025723500108","DOIUrl":"https://doi.org/10.1142/s0219025723500108","url":null,"abstract":"This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts the problem reduces to stochastic Schrodinger equation with space-time white noise of Gaussian, Poisson and Levy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by stochastic nonlinear Schrodinger equation in the focusing case with space-time white noise. A treatment of stochastic transport equation, the Korteweg-de Vries Equation as well as a number of other nonlinear wave equations with space-time white noise is also given. Main technique is the S-transform (we will actually use closely related Hermite transform) which converts the stochastic partial differential equation with space time white noise to a deterministic partial differential equation defined on the Hida-Kondratiev white noise distribution space. We then utlize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for pathwise solutions of these class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of partial differential equations that arise in nonlinear wave propagation have polynomial type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83230737","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 the rate of convergence in the Boolean central limit theorem 关于布尔中心极限定理收敛速度的注解
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-29 DOI: 10.1142/s0219025722500321
Mauricio Salazar
{"title":"A note on the rate of convergence in the Boolean central limit theorem","authors":"Mauricio Salazar","doi":"10.1142/s0219025722500321","DOIUrl":"https://doi.org/10.1142/s0219025722500321","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72883229","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
Matrix-valued Schrodinger operators over finite adeles 有限矩阵上的矩阵值薛定谔算子
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-29 DOI: 10.1142/s021902572250031x
Roman Urban
{"title":"Matrix-valued Schrodinger operators over finite adeles","authors":"Roman Urban","doi":"10.1142/s021902572250031x","DOIUrl":"https://doi.org/10.1142/s021902572250031x","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87426962","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 Stopping Rules for Tree-indexed Quantum Markov chains 树索引量子马尔可夫链的停止规则
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-29 DOI: 10.1142/s0219025722500308
A. Souissi
{"title":"On Stopping Rules for Tree-indexed Quantum Markov chains","authors":"A. Souissi","doi":"10.1142/s0219025722500308","DOIUrl":"https://doi.org/10.1142/s0219025722500308","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86525433","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: 4
Refinements of asymptotics at zero of Brownian self-intersection local times 布朗自交局部时零处渐近性的改进
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-12-29 DOI: 10.1142/s0219025723500182
A. Dorogovtsev, N. Salhi
{"title":"Refinements of asymptotics at zero of Brownian self-intersection local times","authors":"A. Dorogovtsev, N. Salhi","doi":"10.1142/s0219025723500182","DOIUrl":"https://doi.org/10.1142/s0219025723500182","url":null,"abstract":"In this article we establish some estimates related to the Gaussian densities and to Hermite polynomials in order to obtain an almost sure estimate for each term of the It^{o}-Wiener expansion of the self-intersection local times of the Brownian motion. In dimension $dgeqslant 4$ the self-intersection local times of the Brownian motion can be considered as a family of measures on the classical Wiener space. We provide some asymptotics relative to these measures. Finally, we try to estimate the quadratic Wasserstein distance between these measures and the Wiener measure.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86979641","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 non-commutative multifractional Brownian motion 非交换多分数布朗运动
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-11-18 DOI: 10.1142/s0219025722400100
M. Dozzi, R. Schott
{"title":"On the non-commutative multifractional Brownian motion","authors":"M. Dozzi, R. Schott","doi":"10.1142/s0219025722400100","DOIUrl":"https://doi.org/10.1142/s0219025722400100","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86351448","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
Analogues of Poisson Type Limit Theorems in Discrete BM-Fock Spaces 离散BM-Fock空间中泊松极限定理的类似项
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-10-22 DOI: 10.1142/s0219025723500170
Lahcen Oussi, Janusz Wysocza'nski
{"title":"Analogues of Poisson Type Limit Theorems in Discrete BM-Fock Spaces","authors":"Lahcen Oussi, Janusz Wysocza'nski","doi":"10.1142/s0219025723500170","DOIUrl":"https://doi.org/10.1142/s0219025723500170","url":null,"abstract":"We present analogues of the Poisson limit distribution for the noncommutative bm-independence, which is associated with several positive symmetric cones. We construct related discrete Fock spaces with creation, annihilation and conservation operators, and prove Poisson type limit theorems for them. Properties of the positive cones, in particular the volume characteristic property they enjoy, and the combinatorics of labelled noncrossing partitions, play crucial role in these considerations.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88029420","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
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