One-dimensional skew diffusions: explicit expressions of densities and resolvent kernels

Antoine Lejay 1, 2 Lionel Lenôtre 3 Géraldine Pichot 3
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
3 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
Abstract : The study of skew diffusion is of primary concern for their implication in the mod-eling and simulation of diffusion phenomenons in media with interfaces. First, we provide results on one-dimensional processes with discontinuous coefficients and their connections with the Feller theory of generators as well as the oneof stochastic differential equations involving local time. Second, in view of developing new simulation techniques, we give a method to compute the density and the resolvent kernel of skew diffusions which can be extended to Feller processes in general. Explicit closed-form are given for some particular cases.
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Antoine Lejay, Lionel Lenôtre, Géraldine Pichot. One-dimensional skew diffusions: explicit expressions of densities and resolvent kernels. [Research Report] Inria Rennes - Bretagne Atlantique; Inria Nancy - Grand Est. 2015. ⟨hal-01194187v2⟩

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