2021
DOI: 10.48550/arxiv.2107.07838
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Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach

Alexander Kalinin,
Thilo Meyer-Brandis,
Frank Proske

Abstract: We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random coefficients, which are allowed to be non-Lipschitz continuous. In the case of deterministic coefficients we also obtain the existence of unique strong solutions. By using our approach, which is based on an extension of the Yamada-Watanabe ansatz to the multidimensional setting and which does not rely on the construction of Lyapunov functions, we prove first moment and pathwise α-exponential s… Show more

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Cited by 2 publications
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“…) n∈N converges in probability to (X s,x,v t , V s,v t ). By using Lemma 4.2, this can be inferred from Theorem 4.6 in [26], which gives a first moment estimate for random Itô processes and implies the two estimates (4.6) and (4.7).…”
Section: Proofs For the Conditionally Independent Hitting Timesmentioning
confidence: 78%
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“…) n∈N converges in probability to (X s,x,v t , V s,v t ). By using Lemma 4.2, this can be inferred from Theorem 4.6 in [26], which gives a first moment estimate for random Itô processes and implies the two estimates (4.6) and (4.7).…”
Section: Proofs For the Conditionally Independent Hitting Timesmentioning
confidence: 78%
“…(i) The drift and diffusion coefficients of the SDE (4.11) are independent of the first spatial coordinate. For this reason, the claim follows directly from Corollary 3.9, Remark 3.10 and Proposition 3.13 in [26], which yield pathwise uniqueness for the second SDE in (4.1).…”
Section: Proofs For the Conditionally Independent Hitting Timesmentioning
confidence: 85%
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