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 E f(Xtx,y)=E f (x, Yty) 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.
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