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 |
|---|---|
| Article number | 038 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 4 |
| DOIs | |
| Publication status | Published - 6 Apr 2008 |
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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
Cite this
Nonlinear Fokker-Planck equation in the model of asset returns. / Shapovalov, Aleksandr Vasilievich; Trifonov, Andrey; Masalova, Elena.
In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 4, 038, 06.04.2008.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear Fokker-Planck equation in the model of asset returns
AU - Shapovalov, Aleksandr Vasilievich
AU - Trifonov, Andrey
AU - Masalova, Elena
PY - 2008/4/6
Y1 - 2008/4/6
N2 - 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.
AB - 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.
KW - Fokker-Planck equation
KW - Non-linear evolution operator
KW - Semiclassical asymptotics
KW - The cauchy problem
KW - Trajectory concentrated functions
UR - http://www.scopus.com/inward/record.url?scp=84857344199&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84857344199&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2008.038
DO - 10.3842/SIGMA.2008.038
M3 - Article
AN - SCOPUS:84857344199
VL - 4
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 038
ER -