How to determine the law of the solution to a stochastic partial differential equation driven by a Levy space-time noise?

被引:8
|
作者
Gottschalk, Hanno
Smii, Boubaker
机构
[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
[2] Univ Tunis El Manar, Dept Math, TN-1006 Tunis, Tunisia
关键词
D O I
10.1063/1.2712916
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider a stochastic partial differential equation on a lattice partial derivative X-t=(Delta-m(2))X-lambda X-p+eta, where eta is a space-time Levy noise. A perturbative (in the sense of formal power series) strong solution is given by a tree expansion, whereas the correlation functions of the solution are given by a perturbative expansion with coefficients that are represented as sums over a certain class of graphs, called Parisi-Wu graphs. The perturbative expansion of the truncated (connected) correlation functions is obtained via a linked cluster theorem as sums over connected graphs only. The moments of the stationary solution can be calculated as well. In all these solutions the cumulants of the single site distribution of the noise enter as multiplicative constants. To determine them, e.g., by comparison with an empirical correlation function, one can fit these constants (e.g., by the methods of least squares) and thereby one (approximately) determines laws of the solution and the driving noise. (c) 2007 American Institute of Physics.
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页数:22
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