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

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Numerical solution for a class of SPDEs over bounded domains 一类有界域上spde的数值解
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-05-04 DOI: 10.1080/17442508.2013.819510
D. Crisan, J. Xiong
{"title":"Numerical solution for a class of SPDEs over bounded domains","authors":"D. Crisan, J. Xiong","doi":"10.1080/17442508.2013.819510","DOIUrl":"https://doi.org/10.1080/17442508.2013.819510","url":null,"abstract":"Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295–308].","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75649232","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
The Bouleau–Yor identity for a bi-fractional Brownian motion 双分数布朗运动的布洛-你恒等式
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-05-04 DOI: 10.1080/17442508.2013.797424
Litan Yan, Bo Gao, Junfeng Liu
{"title":"The Bouleau–Yor identity for a bi-fractional Brownian motion","authors":"Litan Yan, Bo Gao, Junfeng Liu","doi":"10.1080/17442508.2013.797424","DOIUrl":"https://doi.org/10.1080/17442508.2013.797424","url":null,"abstract":"Let B be a bi-fractional Brownian motion with indices , and let be its local time process. We construct a Banach space of measurable functions such that the quadratic covariation and the integral exist provided . Moreover, the Bouleau–Yor identityholds for all .","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90617075","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: 12
On the lookback option with fixed strike 关于回溯选项与固定罢工
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-05-04 DOI: 10.1080/17442508.2013.837908
Y. Kitapbayev
{"title":"On the lookback option with fixed strike","authors":"Y. Kitapbayev","doi":"10.1080/17442508.2013.837908","DOIUrl":"https://doi.org/10.1080/17442508.2013.837908","url":null,"abstract":"The lookback option with fixed strike in the case of finite horizon was examined with help of the solution to the optimal stopping problem for a three-dimensional Markov process in [P. Gapeev, Discounted optimal stopping for maxima in diffusion models with finite horizon, Electron. J. Probab. 11 (2006), pp. 1031–1048]. The purpose of this paper was to illustrate another derivation of the solution in [P. Gapeev, Discounted optimal stopping for maxima in diffusion models with finite horizon, Electron. J. Probab. 11 (2006), pp. 1031–1048]. The key idea is to use the Girsanov change-of-measure theorem which allows to reduce the three-dimensional optimal stopping problem to a two-dimensional optimal stopping problem with a scaling strike. This approach simplifies the discussion and expressions for the arbitrage-free price and the rational exercise boundary. We derive a closed-form expression for the value function of the two-dimensional problem in terms of the optimal stopping boundary and show that the optimal stopping boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results we obtain the arbitrage-free price and the rational exercise boundary of the option.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73350492","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: 6
Moderate deviations for time-varying dynamic systems driven by non-homogeneous Markov chains with Two-time Scales 双时间尺度非齐次马尔可夫链驱动时变动力系统的中等偏差
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-05-04 DOI: 10.1080/17442508.2013.841695
Qi He, G. Yin
{"title":"Moderate deviations for time-varying dynamic systems driven by non-homogeneous Markov chains with Two-time Scales","authors":"Qi He, G. Yin","doi":"10.1080/17442508.2013.841695","DOIUrl":"https://doi.org/10.1080/17442508.2013.841695","url":null,"abstract":"Motivated by problems arising in time-dependent queues and dynamic systems with random environment, this work develops moderate deviations principles for dynamic systems driven by a fast-varying non-homogeneous Markov chain in continuous time. A distinct feature is that the Markov chain is time dependent or inhomogeneous, so are the dynamic systems. Under irreducibility of the non-homogeneous Markov chain, moderate deviations of a non-homogeneous functional are established first. With the help of a martingale problem formulation and a functional central limit theorem for the two timescale system, both upper and lower bounds of moderate deviations are obtained for the rapidly fluctuating Markovian systems. Then applications to queueing systems and dynamic systems modulated by a fast-varying Markov chain are examined.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86691172","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
On complete moment convergence of weighted sums for arrays of row-wise negatively associated random variables 逐行负相关随机变量数组加权和的完全矩收敛性
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-05-04 DOI: 10.1080/17442508.2013.801971
M. Guo
{"title":"On complete moment convergence of weighted sums for arrays of row-wise negatively associated random variables","authors":"M. Guo","doi":"10.1080/17442508.2013.801971","DOIUrl":"https://doi.org/10.1080/17442508.2013.801971","url":null,"abstract":"Negatively associated (NA) random variables are a more general class of random variables which include a set of independent random variables and have been applied to many practical fields. In this paper, the complete moment convergence of weighted sums for arrays of row-wise NA random variables is investigated. Some sufficient conditions for complete moment convergence of weighted sums for arrays of row-wise NA random variables are established. Moreover, under the weaker conditions, we extend the results of Baek et al. [J. Korean Stat. Soc. 37 (2008), pp. 73–80] and Sung [Abstr. Appl. Anal. 2011 (2011)]. As an application, the complete moment convergence of moving average processes based on an NA random sequence is obtained, which improves the result of Li and Zhang [Stat. Probab. Lett. 70 (2004), pp. 191–197 ].","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73834505","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: 9
Impulse control of a diffusion with a change point 具有变点扩散的脉冲控制
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-04-07 DOI: 10.1080/17442508.2014.956458
L. Abbas-Turki, I. Karatzas, Qinghua Li
{"title":"Impulse control of a diffusion with a change point","authors":"L. Abbas-Turki, I. Karatzas, Qinghua Li","doi":"10.1080/17442508.2014.956458","DOIUrl":"https://doi.org/10.1080/17442508.2014.956458","url":null,"abstract":"This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be expressed in terms of the solutions and the current values of a Markov process adapted to the observation filtration. We shall illustrate the application of our results using the Longstaff–Schwartz algorithm for multiple optimal stopping times in a geometric Brownian motion stock price model with drift uncertainty.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85362636","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
Phase transitions of McKean–Vlasov processes in double-wells landscape 双井景观中McKean-Vlasov过程的相变
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-03-04 DOI: 10.1080/17442508.2013.775287
J. Tugaut
{"title":"Phase transitions of McKean–Vlasov processes in double-wells landscape","authors":"J. Tugaut","doi":"10.1080/17442508.2013.775287","DOIUrl":"https://doi.org/10.1080/17442508.2013.775287","url":null,"abstract":"The aim of this work is to establish the results for a particular class of inhomogeneous processes, the McKean–Vlasov diffusions. Such diffusions correspond to the hydrodynamical limit of an interacting particle system. In convex landscapes, existence and uniqueness of the invariant probability is a well-known result. However, previous results state the nonuniqueness of the invariant probabilities under nonconvexity assumptions. Here, we prove that there exists a phase transition. Below a critical value, there are exactly three invariant probabilities and above another critical value, there is exactly one. Under simple assumptions, these critical values coincide and it is characterized by a simple implicit equation. We also investigate other cases in which phase transitions occur. Finally, we provide numerical estimations of the critical values.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85130992","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: 63
A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions 具有动态边界条件的随机非线性扩散问题的变分方法
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-03-04 DOI: 10.1080/17442508.2013.775284
S. Bonaccorsi, G. Ziglio
{"title":"A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions","authors":"S. Bonaccorsi, G. Ziglio","doi":"10.1080/17442508.2013.775284","DOIUrl":"https://doi.org/10.1080/17442508.2013.775284","url":null,"abstract":"We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of the solution on the boundary. This work provides the existence and uniqueness of the solution and it shows the existence of an ergodic invariant measure for the corresponding transition semigroup; furthermore, under suitable additional assumptions, uniqueness and strong asymptotic stability of the invariant measure are proved.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86497081","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
On existence of solutions of multivalued stochastic differential equations with discontinuous coefficients 系数不连续的多值随机微分方程解的存在性
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-03-04 DOI: 10.1080/17442508.2013.775286
Jing Wu
{"title":"On existence of solutions of multivalued stochastic differential equations with discontinuous coefficients","authors":"Jing Wu","doi":"10.1080/17442508.2013.775286","DOIUrl":"https://doi.org/10.1080/17442508.2013.775286","url":null,"abstract":"The subject of the paper is to find existence conditions of weak solutions to multivalued stochastic differential equations with discontinuous coefficients. First we prove that a non-exploding solution exists when the drift coefficient b satisfies linear growth and the diffusion coefficient σ is uniformly elliptic. On this basis, we continue to obtain a solution (up to the explosion time) in the weak sense under certain local integrability, improving the result of Rozkosz and Słomiński.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78129663","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
Dynkin games in a general framework Dynkin游戏的一般框架
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-03-04 DOI: 10.1080/17442508.2013.850203
M. Kobylanski, M. Quenez, Marc Roger de Campagnolle
{"title":"Dynkin games in a general framework","authors":"M. Kobylanski, M. Quenez, Marc Roger de Campagnolle","doi":"10.1080/17442508.2013.850203","DOIUrl":"https://doi.org/10.1080/17442508.2013.850203","url":null,"abstract":"and j and z are left limited along stopping times at T with fjðT 2Þ 1⁄4 zðT 2Þ} 1⁄4 Y a.s. (and the same remark holds in the case of processes, that is Theorem B.4). Similarly, in Lemma 4.6, the first equality holds a.s. on ft , T} and the second equality on fu , T}. Also, at the end of the proof of Theorem 4.3, the two inequalities concerning E1⁄2Jðu2Þ1C and E1⁄2J0ðu2Þ1C are precised as follows: E1⁄2Jðu2Þ1C # 1⁄2E1⁄2J0ðu2Þ1C þ E1⁄2jðuÞ1C>fu,T} þ E1⁄2jðT Þ1C>fu1⁄4T} ; E1⁄2J 0ðu2Þ1C # 1⁄2E1⁄2Jðu2Þ1C 2 E1⁄2zðuÞ1C>fu,T} 2 E1⁄2zðT Þ1C>fu1⁄4T} ;","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87657814","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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