Systems of nonlinear backward and forward Kolmogorov equations:
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 20-54
Voir la notice de l'article provenant de la source Math-Net.Ru
A probabilistic approach to construction of the solution to the Cauchy problem
for systems of nonlinear parabolic equations is developed. The systems under
consideration can be subdivided into two classes: the systems of the first
class can be interpreted, after a simple transformation, as systems of
nonlinear backward Kolmogorov equations, and the systems of the second class
as systems of nonlinear forward Kolmogorov equations. By choosing an
appropriate interpretation, one can construct a stochastic model in terms of
a stochastic equation with coefficients depending on the solution of the
Cauchy problem under consideration and the closing relation corresponding to
the probabilistic representation of this solution.
Mots-clés :
diffusion processes
Keywords: systems of nonlinear backward and forward Kolmogorov equations, stochastic flows.
Keywords: systems of nonlinear backward and forward Kolmogorov equations, stochastic flows.
@article{TVP_2021_66_1_a1,
author = {Ya. I. Belopol'skaya},
title = {Systems of nonlinear backward and forward {Kolmogorov} equations:},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {20--54},
publisher = {mathdoc},
volume = {66},
number = {1},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a1/}
}
Ya. I. Belopol'skaya. Systems of nonlinear backward and forward Kolmogorov equations:. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 20-54. http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a1/