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• W2463237051 abstract "We consider $mathbb{R}^d$-valued diffusion processes of type begin{align*} dX_t = b(X_t)dt, +, dB_t. end{align*} Assuming a geometric drift condition, we establish contractions of the transitions kernels in Kantorovich ($L^1$ Wasserstein) distances with explicit constants. Our results are in the spirit of Hairer and Mattingly's extension of Harris' Theorem. In particular, they do not rely on a small set condition. Instead we combine Lyapunov functions with reflection coupling and concave distance functions. We retrieve constants that are explicit in parameters which can be computed with little effort from one-sided Lipschitz conditions for the drift coefficient and the growth of a chosen Lyapunov function. Consequences include exponential convergence in weighted total variation norms, gradient bounds, bounds for ergodic averages, and Kantorovich contractions for nonlinear McKean-Vlasov diffusions in the case of sufficiently weak but not necessarily bounded nonlinearities. We also establish quantitative bounds for sub-geometric ergodicity assuming a sub-geometric drift condition." @default.
• W2463237051 created "2016-07-22" @default.
• W2463237051 creator A5030977374 @default.
• W2463237051 creator A5051679487 @default.
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• W2463237051 date "2016-06-20" @default.
• W2463237051 modified "2023-09-25" @default.
• W2463237051 title "Quantitative Harris type theorems for diffusions and McKean-Vlasov processes" @default.
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• W2463237051 hasPublicationYear "2016" @default.
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