Pub Date : 2023-03-10DOI: 10.1142/s0219025723500042
Nenghui Kuang, Huantian Xie
{"title":"Least squares type estimators for the drift parameters in the sub-bifractional Vasicek processes","authors":"Nenghui Kuang, Huantian Xie","doi":"10.1142/s0219025723500042","DOIUrl":"https://doi.org/10.1142/s0219025723500042","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85858256","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 : 2023-03-10DOI: 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":"35 1","pages":""},"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}
Pub Date : 2022-12-31DOI: 10.1142/s0219025722400033
Michael Skeide
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.
{"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":"1182 ","pages":""},"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}
Pub Date : 2022-12-31DOI: 10.1142/s0219025723500108
S. Sritharan, S. Mudaliar
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.
{"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":"22 1","pages":""},"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}
Pub Date : 2022-12-29DOI: 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":"24 1","pages":""},"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}
Pub Date : 2022-12-29DOI: 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":"4 1","pages":""},"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}
Pub Date : 2022-12-29DOI: 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":"7 1","pages":""},"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}
Pub Date : 2022-12-29DOI: 10.1142/s0219025723500182
A. Dorogovtsev, N. Salhi
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.
{"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":"58 1","pages":""},"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}
Pub Date : 2022-11-18DOI: 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":"71 1","pages":""},"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}
Pub Date : 2022-10-22DOI: 10.1142/s0219025723500170
Lahcen Oussi, Janusz Wysocza'nski
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.
{"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":"15 1","pages":""},"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}
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