Abstract
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker-Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leading term of the Cauchy problem solution asymptotic in a formal small parameter in semiclassical approximation following the complex WKB-Maslov method in the class of trajectory concentrated functions.
Original language | English |
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Article number | 038 |
Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
Volume | 4 |
DOIs | |
Publication status | Published - 6 Apr 2008 |
Keywords
- Fokker-Planck equation
- Non-linear evolution operator
- Semiclassical asymptotics
- The cauchy problem
- Trajectory concentrated functions
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Mathematical Physics