Doubling variables and uniqueness of probability solutions to degenerate stationary Kolmogorov equations
V.I. Bogachev, S.V. Shaposhnikov, D.V. Shatilovich
TL;DR
This paper establishes conditions ensuring the uniqueness of probability solutions to degenerate stationary Kolmogorov equations using the doubling variables method from stochastic analysis.
Contribution
It introduces a novel application of the doubling variables technique to prove uniqueness in degenerate Kolmogorov equations.
Findings
Provided sufficient conditions for uniqueness of solutions.
Applied the doubling variables method directly to the Kolmogorov equation.
Extended the understanding of degenerate diffusion processes.
Abstract
We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubling variables known in stochastic analysis directly to the Kolmogorov equation.
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Taxonomy
Topicsstochastic dynamics and bifurcation · Nonlinear Differential Equations Analysis · Stochastic processes and financial applications