Journal Articles Journal of Stochastic Analysis Year : 2021

Transfer of Regularity for Markov Semigroups by Using an Interpolation Technique

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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Dates and versions

hal-02429530 , version 1 (06-01-2020)

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Vlad Bally, Lucia Caramellino. Transfer of Regularity for Markov Semigroups by Using an Interpolation Technique. Journal of Stochastic Analysis , 2021, 2 (3), pp.Article 13. ⟨10.31390/josa.2.3.13⟩. ⟨hal-02429530⟩
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