Stochastic partial differential equations driven by Lévy space-time white noise
Stochastic partial differential equations driven by Lévy space-time white noise
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DOI：
10.1214/105051604000000413
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发表时间：
2004-07
影响因子：
1.8
通讯作者：
A. Løkka;Bernt Oksendal;F. Proske
中科院分区：
文献类型：
--
作者：
A. Løkka;Bernt Oksendal;F. Proske
在本文中，我们开发了一个白色噪声框架的研究随机偏微分方程的d参数（纯跳）Levy白色噪声。作为一个例子，我们使用这个理论来解决随机泊松方程关于任何维d的Levy白色噪声。解是一个显式给出的随机分布过程。我们还表明，如果d\leq 3，那么这个解决方案可以表示为一个经典的随机场在L2（\mu），其中\mu是概率律的Levy过程。我们的理论的出发点是广义Charlier多项式的混沌展开。在此基础上定义了Kondratiev空间和Levy Hermite变换。
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\leq 3, then this solution can be represented as a classical random field in L2(\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.