Stochastic duality of Markov processes: a study via generators

Abstract

The paper is devoted to a systematic study of the duality of processes in the sense that $Ef(X_t^x,y)=Ef(x,Y_t^y)$ for a certain $f$. This classical topic has well known applications in interacting particles, intertwining, superprocesses, stochastic monotonicity, exit - entrance laws, ruin probabilities in finances, etc. Aiming mostly at the case of $f$ depending on the difference of its arguments, we shall give a systematic study of duality via the analysis of the generators of dual Markov processes leading to various results and insights.

References in corpus (1)

• Reflected planar Brownian motions, intertwining relations and crossing probabilities

Cited by in corpus (4)

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• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors