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Théorèmes limites pour certaines fonctionnelles associées aux processus stables dans une classe d'espaces de besov 在一类需求空间中与稳定过程相关的某些函数的极限定理
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290024883
M. A. Ouahra, B. Boufoussi, E. Lakhel
{"title":"Théorèmes limites pour certaines fonctionnelles associées aux processus stables dans une classe d'espaces de besov","authors":"M. A. Ouahra, B. Boufoussi, E. Lakhel","doi":"10.1080/10451120290024883","DOIUrl":"https://doi.org/10.1080/10451120290024883","url":null,"abstract":"Dans cet article nous étudions des théorèmes limites pour les temps locaux des processus stables symétriques en dimension un dans une classe d'espaces de Besov. Ce qui présente une généralisation des résultants de Fitzsimmons Getoor et celui de Rosen pour un processus stable dans l'espace des fonctions continues. Les processus obtenus à la limite sont les dérivées fractionnaires et les transformés de Hilbert des temps locaux. This paper studies limit theorems for the occupation times of one-dimensional symmetric stable processes. Our goals is to extend Fitzsimmons and Getoor's results (Fitzsimmons, P.J., Getoor, R.K. \"Limit theorems and variation properties for fractional derivatives of the local time of stable process,\" Ann. Inst. Henri Poincaré , 28 (2) 1992, pp. 311-333) and those of Rosen (Rosen, J., \"Second Order Limit Laws for the Local Times of Stable Processes\", Séminaire de Probabilité XXV. Lecture Notes in Mathematics , Vol. 1485 (1990) pp. 407-425. Springer: New York), established in the uniform norm, to the Besov norm. The limit processes are fractional derivatives and Hilbert transforms of the stable local time.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126422032","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: 8
Necessary conditions for optimality in relaxed stochastic control problems 松弛随机控制问题最优性的必要条件
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000025925
B. Mezerdi, S. Bahlali
{"title":"Necessary conditions for optimality in relaxed stochastic control problems","authors":"B. Mezerdi, S. Bahlali","doi":"10.1080/1045112021000025925","DOIUrl":"https://doi.org/10.1080/1045112021000025925","url":null,"abstract":"In this paper, we are concerned with optimal control problems where the system is driven by a stochastic differential equation of the Ito type. We study the relaxed model for which an optimal solution exists. This is an extension of the initial control problem, where admissible controls are measure valued processes. Using Ekeland's variational principle and some stability properties of the corresponding state equation and adjoint processes, we establish necessary conditions for optimality satisfied by an optimal relaxed control. This is the first version of the stochastic maximum principle that covers relaxed controls.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124013660","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: 28
Representations of the Brownian snake with drift 带有漂移的布朗蛇的表示
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000025952
R. Abraham, L. Serlet
{"title":"Representations of the Brownian snake with drift","authors":"R. Abraham, L. Serlet","doi":"10.1080/1045112021000025952","DOIUrl":"https://doi.org/10.1080/1045112021000025952","url":null,"abstract":"We consider a path-valued process which is a generalization of the classical Brownian snake introduced by Le Gall. More precisely we add a drift term b to the lifetime process, which may depends on the spatial process. Consequently, this introduces a coupling between the lifetime process and the spatial motion. This process can be obtained from the standard Brownian snake by Girsanov's theorem or by killing of the spatial motion. It can also be viewed as the limit of discrete snakes or, in some special cases, as conditioned Brownian snakes. We also use this process to describe the solutions of the non-linear partial differential equation j u =4 u 2 +4 bu .","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125864657","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: 7
Exact transient analysis of a planar random motion with three directions 平面三方向随机运动的精确瞬态分析
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290019186
A. Di Crescenzo
{"title":"Exact transient analysis of a planar random motion with three directions","authors":"A. Di Crescenzo","doi":"10.1080/10451120290019186","DOIUrl":"https://doi.org/10.1080/10451120290019186","url":null,"abstract":"Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of direction perform an alternating renewal process. We obtain the probability law of the bidimensional stochastic process which describes location and direction of the motion. In the Markovian case when the random times between consecutive changes of direction are exponentially distributed, the transition densities of the motion are explicitly given. These are expressed in term of a suitable modified two-index Bessel function.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114671913","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: 2
About the asymptotic behaviour of continuous vector-valued local martingales and application in multiple linear regression models 连续向量值局部鞅的渐近性及其在多元线性回归模型中的应用
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000039687
A. Darwich
{"title":"About the asymptotic behaviour of continuous vector-valued local martingales and application in multiple linear regression models","authors":"A. Darwich","doi":"10.1080/1045112021000039687","DOIUrl":"https://doi.org/10.1080/1045112021000039687","url":null,"abstract":"We study the asymptotic behaviour of the process d M ¢ m 1 M , where M is an R n -continuous vector local martingale and d M ¢ m 1 is the inverse of its predictable quadratic variation (a matrix-valued process). We also give an application (strong consistency and rate of convergence) to multiple linear regression.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116509873","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
Dynamic programming in stochastic control of systems with delay 时滞系统随机控制中的动态规划
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000060764
B. Larssen
{"title":"Dynamic programming in stochastic control of systems with delay","authors":"B. Larssen","doi":"10.1080/1045112021000060764","DOIUrl":"https://doi.org/10.1080/1045112021000060764","url":null,"abstract":"We consider optimal control problems for systems described by stochastic differential equations with delay (SDDE). We prove a version of Bellman's principle of optimality (the dynamic programming principle) for a general class of such problems. That the class in general means that both the dynamics and the cost depends on the past in a general way. As an application, we study systems where the value function depends on the past only through some weighted average. For such systems we obtain a Hamilton-Jacobi-Bellman partial differential equation that the value function must solve if it is smooth enough. The weak uniqueness of the SDDEs we consider is our main tool in proving the result. Notions of strong and weak uniqueness for SDDEs are introduced, and we prove that strong uniqueness implies weak uniqueness, just as for ordinary stochastic differential equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124000249","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: 102
Local asymptotic normality for multivariate nonlinear AR processes 多元非线性AR过程的局部渐近正态性
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290019221
D. Lai, Xiaobao Wang, J. Wiorkowski
{"title":"Local asymptotic normality for multivariate nonlinear AR processes","authors":"D. Lai, Xiaobao Wang, J. Wiorkowski","doi":"10.1080/10451120290019221","DOIUrl":"https://doi.org/10.1080/10451120290019221","url":null,"abstract":"In this paper, we establish local asymptotic normality (LAN) for the log-likelihood ratio of a class of multivariate nonlinear autoregressive processes generated by independent identically distributed (i.i.d.) random vectors. This result generalizes LAN for multivariate linear processes to multivariate nonlinear autoregressive processes.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127457343","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: 2
Reduction of dimension for spatial point processes and right continuous martingales 空间点过程与右连续鞅的降维
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290008539
G. Aletti, V. Capasso
{"title":"Reduction of dimension for spatial point processes and right continuous martingales","authors":"G. Aletti, V. Capasso","doi":"10.1080/10451120290008539","DOIUrl":"https://doi.org/10.1080/10451120290008539","url":null,"abstract":"A problem of reduction of dimension of planar point processes and martingales is faced here by considering these processes along optional increasing paths. Reparametrization of the optional increasing paths by families of natural time preserves the martingale property and makes the process along the path a one-dimensional Poisson process. A novel characterization of spatial martingales and spatial Poisson processes is so obtained.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126313147","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: 5
Statistical analysis of stochastic resonance with ergodic diffusion noise 具有遍历扩散噪声的随机共振的统计分析
Stochastics and Stochastic Reports Pub Date : 2001-11-13 DOI: 10.1080/1045112021000025943
S. Iacus
{"title":"Statistical analysis of stochastic resonance with ergodic diffusion noise","authors":"S. Iacus","doi":"10.1080/1045112021000025943","DOIUrl":"https://doi.org/10.1080/1045112021000025943","url":null,"abstract":"A subthreshold signal is transmitted through a channel and may be detected when some noise--with known structure and proportional to some level--is added to the data. There is an optimal noise level, called stochastic resonance that corresponds to the highest Fisher information in the problem of estimation of the signal. As noise we consider an ergodic diffusion process and the asymptotic is considered as time goes to infinity. We propose consistent estimators of the subthreshold signal and we solve further a problem of hypotheses testing. We also discuss evidence of stochastic resonance for both estimation and hypotheses testing problems via examples.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130246294","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: 27
Logarithmic derivatives of invariant measure for stochastic differential equations in hilbert spaces 希尔伯特空间中随机微分方程不变测度的对数导数
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834270
M. Fuhrman
{"title":"Logarithmic derivatives of invariant measure for stochastic differential equations in hilbert spaces","authors":"M. Fuhrman","doi":"10.1080/17442500108834270","DOIUrl":"https://doi.org/10.1080/17442500108834270","url":null,"abstract":"We consider a process X solution of a semilinear stochastic evolution equation in a Hilbert space. Assuming that X has an invariant measure ν, we investigate its regularity properties. Logarithmic derivatives of ν in certain directions, are shown to exist under appropriate conditions on the nonlinear term in the equation. A set of directions of differentiability for ν is explicitly described in terms of the coefficients of the equation. In some cases, logarithmic derivatives are represented as conditional expectations of random variables related to an appropriate stationary process. An application to a system of stochastic partial differential equations in one space variable is given","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124077379","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: 2
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