Stochastics and Stochastic Reports最新文献_第7页

Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: The singular case 分数布朗运动下不定Skorohod积分的Besov正则性:奇异情况

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000015304

Hassan Lakhel, Y. Ouknine, C. Tudor

引用次数: 7

Stochastic reaction diffusion equations on an infinite interval with reflection 具有反射的无限区间上的随机反应扩散方程

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290024900

Y. Otobe

引用次数: 7

Limit theorems for BSDE with local time applications to non-linear PDE 局部时间应用于非线性偏微分方程的BSDE极限定理

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120212870

M. Eddahbi, Y. Ouknine

{"title":"Limit theorems for BSDE with local time applications to non-linear PDE","authors":"M. Eddahbi, Y. Ouknine","doi":"10.1080/10451120212870","DOIUrl":"https://doi.org/10.1080/10451120212870","url":null,"abstract":"Given a d -dimensional Wiener process W , with its natural filtration F t , a F T -measurable random variable ξ in R , a bounded measure x on R , and an adapted process ( s , y , z ) M h ( s , y , z ), we consider the following BSDE: Y t = ξ + Z t T h ( s , Y s , Z s ) d s + Z R ( L T a ( Y ) m L t a ( Y )) x (d a ) m Z t T Z s d W s for 0 h t h T . Here L t a ( Y ) stands for the local time of Y at level a . For h =0, we establish the existence and the uniqueness of the processes ( Y , Z ), and if h is continuous with linear growth we establish the existence of a solution. We prove limit theorems for solutions of backward stochastic differential equations of the above form. Those limit theorems permit us to deduce that any solution of that equation is the limit, in a strong sense, of a sequence of semi-martingales, which are solutions of ordinary BSDEs of the form Y t = ξ + Z t T f ( Y s ) Z s 2 d s m Z t T Z s d W s . A comparison theorem for BSDEs involving measures is discussed. As an application we obtain, with the help of the connection between BSDE and PDE, some corresponding limit theorems for a class of singular non-linear PDEs and a new probabilistic proof of the comparison theorem for PDEs.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"85 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":"120841913","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

Differential equations in spaces of abstract stochastic distributions 抽象随机分布空间中的微分方程

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290019177

A. Filinkov, J. Sorensen

引用次数: 26

Stochastic partial differential equations in bounded domains with Dirichlet boundary conditions 具有Dirichlet边界条件的有界区域上的随机偏微分方程

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290024865

S. Bonaccorsi, G. Guatteri

引用次数: 6

Comparison theorems for stochastic evolution equations 随机演化方程的比较定理

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290008566

A. Milian

引用次数: 44

Regularity of the value function and viscosity solutions in optimal stopping problems for general Markov processes 一般马尔可夫过程最优停止问题的值函数和粘性解的正则性

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000015331

Bruno Bassan, Claudia Ceci

引用次数: 15

The Bismut-Elworthy formula for backward SDE's and applications to nonlinear Kolmogorov equations and control in infinite dimensional spaces 后向SDE的Bismut-Elworthy公式及其在无限维空间非线性Kolmogorov方程和控制中的应用

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/104S1120290024856

M. Fuhrman, G. Tessitore

{"title":"The Bismut-Elworthy formula for backward SDE's and applications to nonlinear Kolmogorov equations and control in infinite dimensional spaces","authors":"M. Fuhrman, G. Tessitore","doi":"10.1080/104S1120290024856","DOIUrl":"https://doi.org/10.1080/104S1120290024856","url":null,"abstract":"We consider a forward-backward system of stochastic evolution equations in a Hilbert space. Under nondegeneracy assumptions on the diffusion coefficient (that may be nonconstant) we prove an analogue of the well-known Bismut-Elworthy formula. Next, we consider a nonlinear version of the Kolmogorov equation, i.e. a deterministic quasilinear equation associated to the system according to Pardoux, E and Peng, S. (1992). \"Backward stochastic differential equations and quasilinear parabolic partial differential equations\". In: Rozowskii, B.L., Sowers, R.B. (Eds.), Stochastic Partial Differential Equations and Their Applications , Lecture Notes in Control Inf. Sci., Vol. 176, pp. 200-217. Springer: Berlin. The Bismut-Elworthy formula is applied to prove smoothing effect, i.e. to prove existence and uniqueness of a solution which is differentiable with respect to the space variable, even if the initial datum and (some) coefficients of the equation are not. The results are then applied to the Hamilton-Jacobi-Bellman equation of stochastic optimal control. This way we are able to characterize optimal controls by feedback laws for a class of infinite-dimensional control systems, including in particular the stochastic heat equation with state-dependent diffusion coefficient.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"39 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":"124664864","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: 55

Moderate deviations for martingale differences and applications to φ -mixing sequences 鞅差的中等偏差及其在φ -混炼序列中的应用

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112029001/0941

H. Djellout

{"title":"Moderate deviations for martingale differences and applications to φ -mixing sequences","authors":"H. Djellout","doi":"10.1080/1045112029001/0941","DOIUrl":"https://doi.org/10.1080/1045112029001/0941","url":null,"abstract":"For a R d -valued sequence of martingale differences { m k } k S 1 , we obtain a moderate deviation principle for the sequence of partial sums { Z n ( t ) 1 ~ k =1 [ nt ] m k / b n , t ] [0,1]}, in the space of càdlàg functions equipped with the Skorohod topology, under the following conditions: a Chen-Ledoux type condition, an exponential convergence in probability of the associated quadratic variation process of the martingale, and a condition of \"Lindeberg\" type. For the small jumps of Z n (·), we apply the general result of Puhalskii [Puhalskii, A. (1994). \"Large deviations of semimartingales via convergence of the predictable characteristics\". Stoch. Stoch. Rep. , 49 , pp. 27-85]. Following the method of Ledoux [Ledoux, M. (1992). \"Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi\". Ann. Inst. H. Poincaré , 28 , pp. 267-280] and Arcones [Arcones, A. (1999). \"The large deviation principle for stochastic processes\", Submitted for publication], we prove that the large jumps part of Z n (·) is negligible in the sense of the moderate deviations. One can regard our result as an extension to martingale differences, of the beautiful characterization of moderate deviations for i.i.d.r.v. case due to Chen [Chen, X. (1991). \"The moderate deviations of independent vectors in Banach space\". Chin. J. Appl. Probab. Stat. , 7 , pp. 124-32] and Ledoux [Ledoux, M. (1992). \"Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi\". Ann. Inst. H. Poincaré , 28 , pp. 267-280]. Using the Gordin [Gordin, M.I. (1969). \"The central limit theorem for stationary processes\". Soviet Math. Dokl. , 10 , pp. 1174-1176] decomposition, the martingale result is applied to prove the moderate deviation principle for a wide class of stationary { -mixing sequences of random variables.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"74 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":"121356651","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: 43

Bessel functions of third order and the distribution of cyclic planar motions with three directions 三阶贝塞尔函数与平面三方向循环运动的分布

Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000060755

E. Orsingher

引用次数: 25