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A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input 高斯输入下泛函中心极限定理的急剧收敛速度
Journal of Stochastic Analysis Pub Date : 2022-09-17 DOI: 10.31390/josa.3.3.05
S. Lototsky
{"title":"A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input","authors":"S. Lototsky","doi":"10.31390/josa.3.3.05","DOIUrl":"https://doi.org/10.31390/josa.3.3.05","url":null,"abstract":". When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the Wasserstein-1 metric on the space of continuous functions. Matching upper and lower bounds are established, indicating that the convergence rate is slightly faster than in the L´evy-Prokhorov metric.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121865064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Domain of Exotic Laplacian Constructed by Wiener Integrals of Exponential White Noise Distributions 指数白噪声分布的Wiener积分构造的奇异拉普拉斯域
Journal of Stochastic Analysis Pub Date : 2022-08-25 DOI: 10.31390/josa.3.3.01
L. Accardi, U. Ji, Kimiaki Sait�
{"title":"Domain of Exotic Laplacian Constructed by Wiener Integrals of Exponential White Noise Distributions","authors":"L. Accardi, U. Ji, Kimiaki Sait�","doi":"10.31390/josa.3.3.01","DOIUrl":"https://doi.org/10.31390/josa.3.3.01","url":null,"abstract":"In this paper we introduce a new domain of an exotic Laplacian consisting of some white noise distribution-valued Wiener integrals based on exponential distributions in a Fock space, and give a construction of a stochastic process as an infinite dimensional Brownian motion generated by the exotic Laplacians. The Brownian motion generated by the Gross Laplacian is extended to the stochastic process generated by the Lévy Laplacian on the domain. Moreover we give a relationship between semigroups generated by the exotic Laplacians and the Lévy Laplacian on the new domain.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126074080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Construction and Estimation of Hidden Semi-Markov Models 隐半马尔可夫模型的构造与估计
Journal of Stochastic Analysis Pub Date : 2022-07-27 DOI: 10.31390/josa.3.2.06
Kurdstan Abdullah, John van der Hoek
{"title":"The Construction and Estimation of Hidden Semi-Markov Models","authors":"Kurdstan Abdullah, John van der Hoek","doi":"10.31390/josa.3.2.06","DOIUrl":"https://doi.org/10.31390/josa.3.2.06","url":null,"abstract":". In this article we construct new formulae and algorithms for Hidden semi-Markov models using Regime Switching Models. We shall include the steps and all necessary lemmas. The formulation of the semi-Markov chain generalizes the one used by Ferguson, by allowing the transition prob- abilities to be duration dependent. However Ferguson supposed that the transition matrix does not depend on the sojourn times. We assume that the transition matrix does depend on the sojourn time.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115545267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Thermodynamics of a Stochastic Geometry Model with Applications to Non-Extensive Statistics 随机几何模型的热力学及其在非广泛统计中的应用
Journal of Stochastic Analysis Pub Date : 2022-07-26 DOI: 10.31390/josa.3.2.05
O. Kazemi, A. Pourdarvish, J. Sadeghi
{"title":"The Thermodynamics of a Stochastic Geometry Model with Applications to Non-Extensive Statistics","authors":"O. Kazemi, A. Pourdarvish, J. Sadeghi","doi":"10.31390/josa.3.2.05","DOIUrl":"https://doi.org/10.31390/josa.3.2.05","url":null,"abstract":"We use the escort distribution instead of the original distribution for calculating the moment generating function and the physical quantities in non-extensive statistical mechanics. According to the associated escort distribution, we obtain the moment generating function for some random variables. In the following, we consider the model of continuum percolation in stochastic geometry and percolation theory which is obtained by connecting the Poisson points with a probability that depends on their relative position. Using a formal expression for the probability of the size of a cluster at the origin provided by Penrose, we derive the q-thermodynamic quantities to evaluate these quantities performance in obtaining the critical point when the percolation occurs. Also, by plotting the q-thermodynamic quantities, we show very interesting fluctuations at the critical point.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129863799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantization of the Poisson Type Central Limit Theorem (1) 泊松中心极限定理的量子化(1)
Journal of Stochastic Analysis Pub Date : 2022-07-17 DOI: 10.31390/josa.3.2.04
Y. Lu
{"title":"Quantization of the Poisson Type Central Limit Theorem (1)","authors":"Y. Lu","doi":"10.31390/josa.3.2.04","DOIUrl":"https://doi.org/10.31390/josa.3.2.04","url":null,"abstract":". A sequence of binomial random variables, both classical and algebraic, is modelized in terms of the creation–annihilation operators in a natural way and each of these random variables is a sum of four terms. By taking a proper interacting Fock structure, these random variables verify a certain pre–given (classical, Boolean, free, monotone, anti–monotone, etc) independence and the sum of finite independent binomial random variables formulates the corresponding Bernoulli sequence. With the help of such a structure, the Poisson type central limit theorem is quantized by considering individually the contribution of those four terms to the limit. Moreover, its off–diagonal part gives a quantization of the Laplace–de Moivre type central limit theorem.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133506120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale 矩阵值半鞅随机指数的封闭形式公式
Journal of Stochastic Analysis Pub Date : 2022-07-10 DOI: 10.31390/josa.3.2.03
Peter Kern, Christian M�ller
{"title":"A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale","authors":"Peter Kern, Christian M�ller","doi":"10.31390/josa.3.2.03","DOIUrl":"https://doi.org/10.31390/josa.3.2.03","url":null,"abstract":"We prove a closed form formula for the stochastic exponential of a matrix-valued semimartingale under the assumption that various commutativity conditions are fulfilled. This extends a corresponding result for continuous semimartingales by Yan in [9] to semimartingales with jump parts. We give three examples of a semimartingale in a Lie group setting for which the commutativity conditions are easily verified and explicitly compute their stochastic exponential.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126362903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Induced Matrices: Recurrences and Markov Chains 诱导矩阵:递归和马尔可夫链
Journal of Stochastic Analysis Pub Date : 2022-06-13 DOI: 10.31390/josa.3.2.02
P. Feinsilver
{"title":"Induced Matrices: Recurrences and Markov Chains","authors":"P. Feinsilver","doi":"10.31390/josa.3.2.02","DOIUrl":"https://doi.org/10.31390/josa.3.2.02","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115042035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-Repelling Elastic Manifolds with Low Dimensional Range 低维范围自排斥弹性流形
Journal of Stochastic Analysis Pub Date : 2022-02-28 DOI: 10.31390/josa.3.2.01
C. Mueller, E. Neuman
{"title":"Self-Repelling Elastic Manifolds with Low Dimensional Range","authors":"C. Mueller, E. Neuman","doi":"10.31390/josa.3.2.01","DOIUrl":"https://doi.org/10.31390/josa.3.2.01","url":null,"abstract":"We consider self-repelling elastic manifolds with a domain $[-N,N]^d cap mathbb{Z}^d$, that take values in $mathbb{R}^D$. Our main result states that when the dimension of the domain is $d=2$ and the dimension of the range is $D=1$, the effective radius $R_N$ of the manifold is approximately $N^{4/3}$. This verifies the conjecture of Kantor, Kardar and Nelson [7]. Our results for the case where $d geq 3$ and $D<d$ give a lower bound on $R_N$ of order $N^{frac{1}{D} left(d-frac{2(d-D)}{D+2} right)}$ and an upper bound proportional to $N^{frac{d}{2}+frac{d-D}{D+2}}$. These results imply that self-repelling elastic manifolds with a low dimensional range undergo a significantly stronger stretching than in the case where $d=D$, which was studied by the authors in [10].","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126815990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An Intrinsic Proof of an Extension of Itô’s Isometry for Anticipating Stochastic Integrals 预测随机积分的Itô等距的扩展的内在证明
Journal of Stochastic Analysis Pub Date : 2021-12-14 DOI: 10.31390/josa.2.4.08
H. Kuo, Pujan Shrestha, S. Sinha
{"title":"An Intrinsic Proof of an Extension of Itô’s Isometry for Anticipating Stochastic Integrals","authors":"H. Kuo, Pujan Shrestha, S. Sinha","doi":"10.31390/josa.2.4.08","DOIUrl":"https://doi.org/10.31390/josa.2.4.08","url":null,"abstract":"Itô’s isometry forms the cornerstone of the definition of Itô’s integral and consequently the theory of stochastic calculus. Therefore, for any theory which extends Itô’s theory, it is important to know if the isometry holds. In this paper, we use probabilistic arguments to demonstrate that the extension of the isometry formula contains an extra term for the anticipating stochastic integral defined by Ayed and Kuo. We give examples to illustrate the usage of this formula and to show that the extra term can be positive or negative.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125788612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The n-Dimensional Quadratic Heisenberg Algebra as a “Non–Commutative” sl(2,C) 作为“非交换”的n维二次Heisenberg代数sl(2,C)
Journal of Stochastic Analysis Pub Date : 2021-10-08 DOI: 10.31390/josa.2.4.02
L. Accardi, A. Boukas, Y. Lu
{"title":"The n-Dimensional Quadratic Heisenberg Algebra as a “Non–Commutative” sl(2,C)","authors":"L. Accardi, A. Boukas, Y. Lu","doi":"10.31390/josa.2.4.02","DOIUrl":"https://doi.org/10.31390/josa.2.4.02","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124364995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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