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This article is cited in 1 scientific paper (total in 1 paper)
Nonlinear Fokker–Planck Equation in the Model of Asset Returns
Alexander Shapovalovabc, Andrey Trifonovbc, Elena Masalovab a Tomsk State University, 36 Lenin Ave., 634050 Tomsk, Russia
b Tomsk Polytechnic University, 30 Lenin Ave., 634050 Tomsk, Russia
c Mathematical Physics Laboratory, Tomsk Polytechnic University, 30 Lenin Ave., 634050 Tomsk, Russia
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.
Keywords:
Fokker–Planck equation; semiclassical asymptotics; the Cauchy problem; nonlinear evolution operator; trajectory concentrated functions.
Received: September 30, 2007; in final form March 26, 2008; Published online April 6, 2008
Citation:
Alexander Shapovalov, Andrey Trifonov, Elena Masalova, “Nonlinear Fokker–Planck Equation in the Model of Asset Returns”, SIGMA, 4 (2008), 038, 10 pp.
Linking options:
https://www.mathnet.ru/eng/sigma291 https://www.mathnet.ru/eng/sigma/v4/p38
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