Stochastic partial differential equations driven by Levy space-time white noise

• 成果类型: Article
• 署名作者: Lokka, A; Oksendal, B; Proske, F
• 署名单位: University of Oslo; Norwegian School of Economics (NHH)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2004
• 页码: 1506-1528
• 关键词: calculus; Poisson

摘要

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d less than or equal to 3, then this solution can be represented as a classical random field in L-2(mu), where mu is the probability law of the Levy process. The starting point of our theory is a chaos expansion in terms of generalized Charlier polynomials. Based on this expansion we define Kondratiev spaces and the Levy Hermite transform.