On uniqueness of solutions to nonlinear Fokker--Planck--Kolmogorov equations
Oxana A. Manita, Maxim S. Romanov, Stanislav V. Shaposhnikov
TL;DR
This paper investigates the conditions under which solutions to nonlinear Fokker-Planck-Kolmogorov equations are unique, providing criteria for uniqueness and examples demonstrating non-uniqueness.
Contribution
It offers new sufficient conditions for the uniqueness of solutions and constructs examples illustrating non-uniqueness in nonlinear Fokker-Planck-Kolmogorov equations.
Findings
Sufficient conditions for solution uniqueness identified
Examples of non-uniqueness constructed
Analysis applicable to equations with unbounded coefficients
Abstract
We study uniqueness of flows of probability measures solving the Cauchy problem for nonlinear Fokker-Planck-Kolmogorov equation with unbounded coefficients. Sufficient conditions for uniqueness are indicated and examples of non-uniqueness are constructed.
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Taxonomy
TopicsStochastic processes and financial applications · Navier-Stokes equation solutions · advanced mathematical theories