Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels

• Autores: Max Fathi, Dan Mikulincer
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 23, Nº 3, 2022, págs. 1417-1445
• Idioma: inglés
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• Resumen

  • We investigate stability of invariant measures of diffusion processes with respect to Lp distances on the coefficients, under an assumption of log- concavity. The method is a variant of a technique introduced by Crippa and De Lellis to study transport equations. As an application, we prove a partial extension of an inequality of Ledoux, Nourdin and Peccati relating transport distances and Stein discrepancies to a non-Gaussian setting via the moment map construction of Stein kernels.