Exit problems for positive self-similar Markov processes with one-sided jumps

Matija Vidmar

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arXiv · 1807.00486

Exit problems for positive self-similar Markov processes with one-sided jumps

Matija Vidmar

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Abstract

A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\'evy processes that underly the pssMp through the Lamperti transform. This theory is then brought to bear on solving the spatio-temporal: (i) two-sided exit problem; (ii) joint first passage problem upwards for the the pssMp and its multiplicative drawdown (resp. drawup) in the spectrally negative (resp. positive) case.

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Matija Vidmar. 2018-07-02. Exit problems for positive self-similar Markov processes with one-sided jumps. https://arxiv.org/abs/1807.00486

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