A perturbative approach to a class of Fokker-Planck equations
| Autor: | Choon-Lin Ho, Yan-Min Dai |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: |
Physics
Class (set theory) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Condensed Matter Physics Space (mathematics) Schrödinger equation Connection (mathematics) Condensed Matter - Other Condensed Matter symbols.namesake Mathematics - Analysis of PDEs FOS: Mathematics symbols Fokker–Planck equation Statistical physics Diffusion (business) Constant (mathematics) Drift coefficient Mathematical Physics Other Condensed Matter (cond-mat.other) Analysis of PDEs (math.AP) |
| Popis: | In this paper we present a direct perturbative method to solving certain Fokker-Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between the Fokker-Planck and Schr\"odinger equations. Two examples are used to illustrate the method. In the first example the drift coefficient depends only on time but not on space. In the second example we consider the Uhlenbeck-Ornstein process with a small drift coefficient. These examples show that the such perturbative approach can be a useful tool to obtain approximate solutions of Fokker-Planck equations with constant diffusion coefficients. Comment: 5 pages, no figures |
| Databáze: | OpenAIRE |
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