14 September 2022 at 16:00

Organised in collaboration with the School of Mathematics, University of Bristol, UK

Stability of Positive Semigroups and their Mean Field Interpretations

Pierre Del Moral, INRIA at the University of Bordeaux, France

This talk is concerned with the stability of positive semigroups and their mean field particle interpretations.

We present a stochastic interpolation methodology based on backward semigroup techniques to obtain sharp quantitative estimates uniformly with respect to the time parameter. The stability analysis discussed in this talk is based on the extension of V-norm contraction methods for Markov operators, to nonlinear normalized semigroups. In the context of unnormalized models, we also present extensions of Perron-Frobenius and Krein-Rutman theorems for positive operators to time-varying positive semigroups.

We illustrate the impact of these stochastic perturbation techniques in the context of diffusion Monte Carlo ground state calculation, Feynman-Kac branching particle interpretations as well as McKean-Vlasov interacting diffusions.

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