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Discretization error of irregular sampling approximations of stochastic integrals

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 296-306页

作者： ZHOU Li-kai SU Zhong-gen Department of Mathematics Zhejiang University

This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.

关键词： Euler scheme irregular sampling stochastic integral weak convergence hedging error

stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

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Science China Mathematics 2012年第11期55卷 2195-2203页

作者： CHEN ChuanZhong MA Li SUN Wei School of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China Department of Mathematics and Statistics Concordia UniversityMontreal H3G 1M8Canada

Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the ext... 详细信息

关键词： non-symmetric Dirichlet form Fukushima's decomposition continuous additive functional of zeroenergy stochastic integral Ito's formula

GAUSSIAN OPERATORS AND SKOROHOD integralS OF RANDOM FIELDS(Ⅱ)

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Chinese Science Bulletin 1992年第12期37卷 972-974页

作者：张荫南 Institute of Mathematics Fudan UniversityShanghai 200433PRC

The present note is a continuation of [1]. We will give a method for calculating the Skorohod integrals and the concept of stochastic derivatives for random fields. Based on them, some kind of generalization of It for... 详细信息

关键词： random field stochastic integral Gaussian measure Ito formula

Ito Formula for integral Processes Related to Space-Time Levy Noise

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Applied Mathematics 2015年第10期6卷 1755-1768页

作者： Raluca M.Balan Cheikh B.Ndongo Department of Mathematics and Statistics University of OttawaOttawaCanada

In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.

关键词： Levy Processes Poisson Random Measure stochastic integral Ito Formula Ito Representation Theorem