Exit distributions for symmetric Markov processes via Gaussian techniques

Abstract

We derive the distribution of the first exit value for a class of symmetric real-valued Markov processes with finite Green's functions using prediction theory for Gaussian processes and Dynkin's theory which relates Markov and Gaussian processes. For Lévy processes with exponential lifetime this method allows us to easily rederive Rogozin's infinitely divisible factorization and to obtain the Fourier transform of the distribution of the first exit value.