Theory of Probability and Mathematical Statistics
Existence and uniqueness theorems for solutions of McKean-Vlasov stochastic equations
Yu.S. Mishura, A.Yu. Veretennikov
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Abstract: New weak and strong existence and weak and strong uniqueness results for the solutions of multi-dimensional stochastic McKean-Vlasov equation are established under relaxed regularity conditions. Weak existence requires a non-degeneracy of diffusion and no more than a linear growth of both coefficients in the state variable. Weak and strong uniqueness are established under the restricted assumption of diffusion, yet without any regularity of the drift; this part is based on the analysis of the total variation metric.
Keywords: Stochastic Itô-McKean-Vlasov equation, weak and strong existence, weak and strong uniqueness, relaxed regularity conditions
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