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Noncommutative quantum decomposition of Gegenbauer white noise process Gegenbauer白噪声过程的非交换量子分解
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-08-31 DOI: 10.1142/s0219025722500187
A. Riahi
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引用次数: 0
Wilhelm von Waldenfels (2-3-1932 - 12-3-2021), a pioneer of quantum probability 威廉·冯·瓦尔登费尔斯(2-3-1932 - 12-3-2021)，量子概率论的先驱
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-08-30 DOI: 10.1142/s0219025722500163
L. Accardi
{"title":"Wilhelm von Waldenfels (2-3-1932 - 12-3-2021), a pioneer of quantum probability","authors":"L. Accardi","doi":"10.1142/s0219025722500163","DOIUrl":"https://doi.org/10.1142/s0219025722500163","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79313881","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
Ergodic Theorems for Higher Order Cesaro Means 高阶Cesaro均值的遍历定理
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-08-30 DOI: 10.1142/s0219025722500151
L. Accardi, B. Choi, U. Ji
{"title":"Ergodic Theorems for Higher Order Cesaro Means","authors":"L. Accardi, B. Choi, U. Ji","doi":"10.1142/s0219025722500151","DOIUrl":"https://doi.org/10.1142/s0219025722500151","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77427596","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
Non-commutative stochastic processes with independent increments 具有独立增量的非交换随机过程
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-07-12 DOI: 10.1142/s0219025722400094
M. Schurmann
{"title":"Non-commutative stochastic processes with independent increments","authors":"M. Schurmann","doi":"10.1142/s0219025722400094","DOIUrl":"https://doi.org/10.1142/s0219025722400094","url":null,"abstract":"This article is on the research of Wilhelm von Waldenfels in the mathematical field of quantum (or non-commutative) probability theory. Wilhelm von Waldenfels cer-tainly was one of the pioneers of this field. His idea was to work with moments and to replace polynomials in commuting variables by free algebras which play the role of algebras of polynomials in non-commuting quantities. Before he contributed to quantum probability he already worked with free algebras and free Lie algebras. One can imagine that this helped to create his own special algebraic method which proved to be so very fruitful. He came from physics. His PhD thesis, supervised by Heinz K¨onig, was in probability theory, in the more modern and more algebraic branch of probability theory on groups. Maybe the three, physics, abstract algebra and probability, must have been the best prerequisites to become a pioneer, even one of the founders, of quantum probability. We concentrate on a small part of the scientific work of Wilhelm von Waldenfels. The aspects of physics are practically not mentioned at all. There is nothing on his results in classical probability on groups (Waldenfels operators). This is an attempt to show how the concepts of non-commutative notions of independence and of L´evy processes on structures like Hopf algebras developed from the ideas of Wilhelm von Waldenfels.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84161013","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
Characterization of Gaussian Quantum Markov Semigroups 高斯量子马尔可夫半群的刻画
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-07-08 DOI: 10.1142/s021902572250014x
D. Poletti
{"title":"Characterization of Gaussian Quantum Markov Semigroups","authors":"D. Poletti","doi":"10.1142/s021902572250014x","DOIUrl":"https://doi.org/10.1142/s021902572250014x","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88135115","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: 2
Some thoughts on Wilhelm von Waldenfels and on universal second order constructions 关于瓦尔登费尔斯和普适二阶结构的一些思考
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-07-08 DOI: 10.1142/s0219025722400082
R. Speicher
{"title":"Some thoughts on Wilhelm von Waldenfels and on universal second order constructions","authors":"R. Speicher","doi":"10.1142/s0219025722400082","DOIUrl":"https://doi.org/10.1142/s0219025722400082","url":null,"abstract":"to Wilhelm for showing me mathematics","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74295815","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
Central limit theorems for heat equation with time-independent noise: the regular and rough cases 含时无关噪声热方程的中心极限定理:正则和粗糙情况
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-05-26 DOI: 10.1142/s0219025722500291
R. Balan, Wangjun Yuan
{"title":"Central limit theorems for heat equation with time-independent noise: the regular and rough cases","authors":"R. Balan, Wangjun Yuan","doi":"10.1142/s0219025722500291","DOIUrl":"https://doi.org/10.1142/s0219025722500291","url":null,"abstract":"In this article, we investigate the asymptotic behaviour of the spatial integral of the solution to the parabolic Anderson model with time independent noise in dimension d ≥ 1, as the domain of the integral becomes large. We consider 3 cases: (a) the case when the noise has an integrable covariance function; (b) the case when the covariance of the noise is given by the Riesz kernel; (c) the case of the rough noise, i.e. fractional noise with index H ∈ ( 14 , 12 ) in dimension d = 1. In each case, we identify the order of magnitude of the variance of the spatial integral, we prove a quantitative central limit theorem for the normalized spatial integral by estimating its total variation distance to a standard normal distribution, and we give the corresponding functional limit result.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83058785","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: 3
Analysis of Space Dependent Noise Functionals with an Application to Linearly Correlated Processes 空间相关噪声泛函的分析及其在线性相关过程中的应用
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-05-25 DOI: 10.1142/s0219025722500114
Yun-Ching Chang, Hsin-Hung Shih
{"title":"Analysis of Space Dependent Noise Functionals with an Application to Linearly Correlated Processes","authors":"Yun-Ching Chang, Hsin-Hung Shih","doi":"10.1142/s0219025722500114","DOIUrl":"https://doi.org/10.1142/s0219025722500114","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89535240","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
Algebraic Central Limit Theorems: A Personal View on One of Wilhelm's Legacies 代数中心极限定理:威廉遗作之一的个人观点
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-05-23 DOI: 10.1142/s0219025722500138
Michael Skeide
{"title":"Algebraic Central Limit Theorems: A Personal View on One of Wilhelm's Legacies","authors":"Michael Skeide","doi":"10.1142/s0219025722500138","DOIUrl":"https://doi.org/10.1142/s0219025722500138","url":null,"abstract":"Bringing forward the concept of convergence in moments from classical random variables to quantum random variables is what 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.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86999256","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
Biorthogonal Approach to Infinite Dimensional Fractional Poisson Measure 无限维分数泊松测度的双正交方法
IF 0.9 4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-05-06 DOI: 10.1142/s0219025723500157
Jerome B. Bendong, Sheila M. Menchavez, Jose Luis da Silva
{"title":"Biorthogonal Approach to Infinite Dimensional Fractional Poisson Measure","authors":"Jerome B. Bendong, Sheila M. Menchavez, Jose Luis da Silva","doi":"10.1142/s0219025723500157","DOIUrl":"https://doi.org/10.1142/s0219025723500157","url":null,"abstract":"In this paper we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure $pi_{sigma}^{beta}$, $0<betaleq1$, on the dual of Schwartz test function space $mathcal{D}'$. The Hilbert space $L^{2}(pi_{sigma}^{beta})$ of complex-valued functions is described in terms of a system of generalized Appell polynomials $mathbb{P}^{sigma,beta,alpha}$ associated to the measure $pi_{sigma}^{beta}$. The kernels $C_{n}^{sigma,beta}(cdot)$, $ninmathbb{N}_{0}$, of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to the system $mathbb{P}^{sigma,beta,alpha}$, there is a generalized dual Appell system $mathbb{Q}^{sigma,beta,alpha}$ that is biorthogonal to $mathbb{P}^{sigma,beta,alpha}$. The test and generalized function spaces associated to the measure $pi_{sigma}^{beta}$ are completely characterized using an integral transform as entire functions.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87560546","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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