More on the long time stability of Feynman-Kac semigroups - Archive ouverte HAL
Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2021

More on the long time stability of Feynman-Kac semigroups

Résumé

Feynman-Kac semigroups appear in various areas of mathematics: non-linear filtering, large deviations theory, spectral analysis of Schrodinger operators among others. Their long time behavior provides important information, for example in terms of ground state energy of Schrodinger operators, or scaled cumulant generating function in large deviations theory. In this paper, we propose a simple and natural extension of the stability of Markov chains for these non-linear evolutions. As other classical ergodicity results, it relies on two assumptions: a Lyapunov condition that induces some compactness, and a minorization condition ensuring some mixing. We show that these conditions are satisfied in a variety of situations. We also show that our technique provides uniform in the time step convergence estimates for discretizations of stochastic differential equations.

Dates et versions

hal-01911620 , version 1 (02-11-2018)

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Grégoire Ferré, Mathias Rousset, Gabriel Stoltz. More on the long time stability of Feynman-Kac semigroups. Stochastics and Partial Differential Equations: Analysis and Computations, 2021, 9 (3), pp.630-673. ⟨10.1007/s40072-020-00178-3⟩. ⟨hal-01911620⟩
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