Numerical analysis and applications of Fokker-Planck equations with multiplicative L\'evy noises
Year: 2018
Type: preprint
Abstract: The Fokker-Planck equations (FPEs) for stochastic systems driven by additivesymmetric $\alpha$-stable L\'evy noise may not adequately describe the time
evolution for the probability density of solution paths in practical
applications, such as hydrodynamical systems, porous media, and composite
materials. As a continuation of previous works on additive case, the FPEs with
multiplicative symmetric $\alpha$-stable L\'evy noises are derived by the
adjoint operator method in the present paper. A new numerical scheme for
solving nonlocal FPEs is constructed, which is shown to satisfy a discrete
maximum principle and to be convergent. Moreover, some examples are given to
illustrate this method. For asymmetric case, general finite difference schemes
are proposed. Furthermore, the corresponding result is successfully applied to
the nonlinear filtering problem.
Source: arXiv (Cornell University)
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3205791518