Nonlinear Fokker-Planck Equation in the Model of Asset Returns
AbstractThe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0804.0900.
Date of creation: Apr 2008
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Publication status: Published in SIGMA 4 (2008), 038, 10 pages
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Web page: http://arxiv.org/
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