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Stochastics-An International Journal of Probability and Stochastic Processes最新文献

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A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables 广义随机变量抛物型随机偏微分方程有限元近似的先验误差估计
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-02-19 DOI: 10.1080/17442508.2014.989526
Christophe Audouze, P. Nair
{"title":"A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables","authors":"Christophe Audouze, P. Nair","doi":"10.1080/17442508.2014.989526","DOIUrl":"https://doi.org/10.1080/17442508.2014.989526","url":null,"abstract":"We consider finite element approximations of parabolic stochastic partial differential equations (SPDEs) in conjunction with the -weighted temporal discretization scheme. We study the stability of the numerical scheme and provide a priori error estimates, using a result of Galvis and Sarkis [Approximating infinity-dimensional stochastic Darcy's equations without uniform ellipticity, SIAM J. Numer. Anal. 47(5) (2009), pp. 3624–3651] on elliptic SPDEs.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74963051","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
A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients 一类具有超线性增长和非lipschitz系数的随机微分方程
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-02-17 DOI: 10.1080/17442508.2015.1012080
K. Bahlali, Antoine Hakassou, Y. Ouknine
{"title":"A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients","authors":"K. Bahlali, Antoine Hakassou, Y. Ouknine","doi":"10.1080/17442508.2015.1012080","DOIUrl":"https://doi.org/10.1080/17442508.2015.1012080","url":null,"abstract":"The purpose of this paper is to study some properties of solutions to one-dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth and non-Lipschitz conditions on the coefficients. Taking inspiration from [K. Bahlali, E.H. Essaky, M. Hassani, and E. Pardoux Existence, uniqueness and stability of backward stochastic differential equation with locally monotone coefficient, C.R.A.S. Paris. 335(9) (2002), pp. 757–762; K. Bahlali, E. H. Essaky, and H. Hassani, Multidimensional BSDEs with super-linear growth coefficients: Application to degenerate systems of semilinear PDEs, C. R. Acad. Sci. Paris, Ser. I. 348 (2010), pp. 677-682; K. Bahlali, E. H. Essaky, and H. Hassani, p-Integrable solutions to multidimensional BSDEs and degenerate systems of PDEs with logarithmic nonlinearities, (2010). Available at arXiv:1007.2388v1 [math.PR]], we introduce a new local condition which ensures the pathwise uniqueness, as well as the non-contact property. We moreover show that the solution produces a stochastic flow of continuous maps and satisfies a large deviations principle of Freidlin–Wentzell type. Our conditions on the coefficients go beyond the existing ones in the literature. For instance, the coefficients are not assumed uniformly continuous and therefore cannot satisfy the classical Osgood condition. The drift coefficient could not be locally monotone and the diffusion is neither locally Lipschitz nor uniformly elliptic. Our conditions on the coefficients are, in some sense, near the best possible. Our results are sharp and mainly based on Gronwall lemma and the localization of the time parameter in concatenated intervals.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83838255","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: 4
Estimates for the diameter of a martingale 鞅的直径估计
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-13 DOI: 10.1080/17442508.2014.939977
A. Osȩkowski
{"title":"Estimates for the diameter of a martingale","authors":"A. Osȩkowski","doi":"10.1080/17442508.2014.939977","DOIUrl":"https://doi.org/10.1080/17442508.2014.939977","url":null,"abstract":"We establish sharp weak type and logarithmic estimates for the diameter of the stopped Brownian motion. Then, using standard embedding theorems, we extend the results to the case of general real-valued continuous-path martingales. The proof rests on finding of the solutions to the corresponding three-dimensional optimal stopping problems.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73438242","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
Complete convergence for weighted sums of LNQD random variables LNQD随机变量加权和的完全收敛性
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.931959
A. Shen, H. Zhu, R. Wu, Y. Zhang
{"title":"Complete convergence for weighted sums of LNQD random variables","authors":"A. Shen, H. Zhu, R. Wu, Y. Zhang","doi":"10.1080/17442508.2014.931959","DOIUrl":"https://doi.org/10.1080/17442508.2014.931959","url":null,"abstract":"In this paper, we study the complete convergence for weighted sums of linearly negative quadrant dependent (LNQD) random variables based on the exponential bounds. In addition, we present some complete convergence for arrays of rowwise LNQD random variables.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76263481","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: 7
Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure 由布朗运动和泊松随机测度驱动的马尔可夫切换倒向随机微分方程
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.914514
Jingtao Shi, Zhen Wu
{"title":"Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure","authors":"Jingtao Shi, Zhen Wu","doi":"10.1080/17442508.2014.914514","DOIUrl":"https://doi.org/10.1080/17442508.2014.914514","url":null,"abstract":"This paper is concerned with backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure. The motivation is a constrained stochastic Riccati equation derived from a stochastic linear quadratic optimal control problem with both Poisson and Markovian jumps. The existence and uniqueness of an adapted solution under global Lipschitz condition on the generator is obtained. The continuous dependence of the solution on parameters is proved. Two comparison theorems are also derived by a generalized Girsanov transformation theorem.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89157940","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: 5
On the predictable representation property of martingales associated with Lévy processes 与lsamvy过程相关的鞅的可预测表示性质
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.932051
P. Di Tella, H. Engelbert
{"title":"On the predictable representation property of martingales associated with Lévy processes","authors":"P. Di Tella, H. Engelbert","doi":"10.1080/17442508.2014.932051","DOIUrl":"https://doi.org/10.1080/17442508.2014.932051","url":null,"abstract":"We investigate the predictable representation property (PRP) in the frame of Lévy processes. To give a general definition of the PRP, we make use of the theory of stable subspaces. Let L be a Lévy process with Lévy measure . The main result is that any total system in leads to a family of martingales with the PRP.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73495711","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: 7
Large deviations for neutral functional SDEs with jumps 具有跳跃的中性功能SDEs的大偏差
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.914516
J. Bao, C. Yuan
{"title":"Large deviations for neutral functional SDEs with jumps","authors":"J. Bao, C. Yuan","doi":"10.1080/17442508.2014.914516","DOIUrl":"https://doi.org/10.1080/17442508.2014.914516","url":null,"abstract":"In this paper, by the weak convergence method, based on a variational representation for positive functionals of a Poisson random measure and Brownian motion, we establish uniform large deviation principles (LDPs) for a class of neutral stochastic differential equations driven by jump processes. As a byproduct, we also obtain uniform LDPs for neutral stochastic differential delay equations which, in particular, allow the coefficients to be highly nonlinear with respect to the delay argument.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74105404","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: 44
Stochastic Volterra integro-differential equations driven by fractional Brownian motion in a Hilbert space 希尔伯特空间中分数布朗运动驱动的随机Volterra积分微分方程
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.924938
N. Dung
{"title":"Stochastic Volterra integro-differential equations driven by fractional Brownian motion in a Hilbert space","authors":"N. Dung","doi":"10.1080/17442508.2014.924938","DOIUrl":"https://doi.org/10.1080/17442508.2014.924938","url":null,"abstract":"In this article, we consider a class of stochastic Volterra integro-differential equations with infinite delay and impulsive effects, driven by fractional Brownian motion with the Hurst index in a Hilbert space. The cases of Lipschitz and bounded impulses are studied separately. The existence and uniqueness of mild solutions are proved by using different fixed-point theorems. An example is given to illustrate the theory.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78525239","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: 17
On the differential equation satisfied by the random measure density of a jump-type Fleming–Viot process 跳跃型Fleming-Viot过程的随机测量密度所满足的微分方程
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.915972
T. T. da Silva, M. Fragoso
{"title":"On the differential equation satisfied by the random measure density of a jump-type Fleming–Viot process","authors":"T. T. da Silva, M. Fragoso","doi":"10.1080/17442508.2014.915972","DOIUrl":"https://doi.org/10.1080/17442508.2014.915972","url":null,"abstract":"The subject matter of this paper is the so-called jump-type Fleming–Viot process. The main result shows that the density of the process has a representation as the solution of a stochastic partial differential equation. When reduced to the Fleming–Viot process, our result recovers the result of N. Konno and T. Shiga [Stochastic partial differential equations for some measure-valued diffusions, Probab. Theory Relat. Fields 79 (1988), pp. 201–225].","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90576016","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
Combined probabilistic algorithm for solving high dimensional problems 求解高维问题的组合概率算法
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI: 10.1080/17442508.2014.914515
R. Farnoosh, Mahboubeh Aalaei, M. Ebrahimi
{"title":"Combined probabilistic algorithm for solving high dimensional problems","authors":"R. Farnoosh, Mahboubeh Aalaei, M. Ebrahimi","doi":"10.1080/17442508.2014.914515","DOIUrl":"https://doi.org/10.1080/17442508.2014.914515","url":null,"abstract":"The present study establishes an accurate and efficient algorithm based on Monte Carlo (MC) simulation for solving high dimensional linear systems of algebraic equations (LSAEs) and two-dimensional Fredholm integral equations of the second kind (FIESK). This new combined numerical-probabilistic algorithm is based on Jacobi over-relaxation method and MC simulation in conjunction with the iterative refinement technique to find the unique solution of the large sparse LSAEs. It has an excellent accuracy, low cost and simple structure. Theoretical results are established to justify the convergence of the algorithm. To confirm the accuracy and efficiency of the present work, the proposed algorithm is used for solving and LSAEs. Furthermore, the algorithm is coupled with Galerkin's method to illustrate the power and effectiveness of the proposed algorithm for solving two-dimensional FIESK.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74850404","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
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