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Almost sure contraction for diffusions on Rd. Application to generalized Langevin diffusions

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  • Monmarché, Pierre

Abstract

In the case of diffusions on Rd with constant diffusion matrix, without assuming reversibility nor hypoellipticity, we prove that the contractivity of the deterministic drift is equivalent to the constant rate contraction of Wasserstein distances Wp, p∈[1,∞]. It also implies concentration inequalities for ergodic means of the process. Such a contractivity property is then established for some non-equilibrium chains of anharmonic oscillators and for some generalized Langevin diffusions when the potential is convex with bounded Hessian and the friction is sufficiently high. This extends previous known results for the usual (kinetic) Langevin diffusion.

Suggested Citation

  • Monmarché, Pierre, 2023. "Almost sure contraction for diffusions on Rd. Application to generalized Langevin diffusions," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 316-349.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:316-349
    DOI: 10.1016/j.spa.2023.04.006
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