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Transfer of regularity for Markov semigroups

Vlad Bally 1, 2 Lucia Caramellino 3 
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : We study the regularity of a Markov semigroup (P t) t>0 , that is, when P t (x, dy) = p t (x, y)dy for a suitable smooth function p t (x, y). This is done by transferring the regularity from an approximating Markov semigroup sequence (P n t) t>0 , n ∈ N, whose associated densities p n t (x, y) are smooth and can blow up as n → ∞. We use an interpolation type result and we show that if there exists a good equilibrium between the blow up and the speed of convergence, then P t (x, dy) = p t (x, y)dy and p t has some regularity properties.
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Vlad Bally, Lucia Caramellino. Transfer of regularity for Markov semigroups. Journal of Stochastic Analysis , Louisiana State University, 2021, 2 (3), pp.Article 13. ⟨hal-02429530⟩



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