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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

A Nonstandard Lévy-Khintchine Formula and Lévy processes

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Acta Mathematica Sinica,English Series 2008年第2期24卷 241-252页

作者： Siu Ah NG School of Mathematical Sciences University of KwaZulu-Natal Pietermaritzburg 3209 South Africa

We use methods from nonstandard analysis to obtain a short and simple derivation of the levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary... 详细信息

关键词： levy processes levy-Khintchine formula nonstandard analysis infinitesimal hyperfinite

Option Pricing for Time-Change Exponential Lévy Model Under Memm

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 651-664页

作者： Xu Chen Jian-ping Wan Department of Mathematics Hunan Normal University Changsha 410081 China Department of Mathematics Huazhong University of Science & Technology Wuhan 430074 China

The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change levy process. European option pricing formula is obtained under the minimal entropy martingale measure （MEMM） and applied to several examples of particular time-change levy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.

关键词： Option pricing levy processes time-change subordination MEMM

Stochastic Generalized Porous Media Equations with levy Jump

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1671-1696页

作者： Guo Li ZHOU Zhen TingHOU College of Mathematics and Statistics Chongqing University Chongqing 401331 P. R. China and School of Mathematics Central South University Changsha 410075 P. R. China School of Mathematics Central South University Changsha 410075 P. R. China

In this paper, we first prove the existence and uniqueness of a general stochastic differential equation in finite dimension, then extend the result to the infinite dimension by the classical Galerkin method. As an application, we prove the existence and uniqueness of the generalized stochastic porous medium equation perturbed by levy process.

关键词： Stochastic porous medium equation levy processes

The Ergodicity of Stochastic Partial Differential Equations with levy Jump

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Acta Mathematica Sinica,English Series 2011年第12期27卷 2415-2436页

作者： Guo Li ZHOU Zhen Ting HOU College of Mathematics and Statistics Chongqing University Chongqing 401331 P. R. China School of Mathematics Central South University Changsha 410075 P. R. China

In this article, the authors prove the uniqueness in law of a class of stochastic equations in infinite dimension, then we apply it to establish the existence and uniqueness of invariant measure of the generalized sto... 详细信息

关键词： Stochastic partial differential equation levy processes

Mild Solution of Stochastic Equations with levy Jumps： Existence, Uniqueness, Regularity and Stability

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Journal of Partial Differential Equations 2013年第3期26卷 251-288页

作者： ZHOU Guoli GUO Boling HOU Zhenting College of Mathematics and Statistics Chong Qing University Chong Qing 401331China. Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China. College of Mathematics and Statistics Central South University Changsha 410075 China.

The existence and uniqueness of mild solution to stochastic equations with jumps are established a stochastic Fubini theorem and a type of Burkholder-DavisGundy inequality are proved and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by levy process. Then the authors prove the moment exponential stability almost sure exponential stability and comparison principles of the mild solution. As applications the stability and comparison principles of stochastic heat equation with levy jump are given.

关键词： Stochastic evolution equation levy processes mild solution stability