A temporal factorization at the maximum for spectrally negative positive self-similar Markov processes

Matija Vidmar

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arXiv · 1805.04036

A temporal factorization at the maximum for spectrally negative positive self-similar Markov processes

Matija Vidmar

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Abstract

For a spectrally negative positive self-similar Markov process with an a.s. finite overall supremum we provide, in tractable detail, a kind of conditional Wiener-Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of said absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existent results in the literature.

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Matija Vidmar. 2018-05-10. A temporal factorization at the maximum for spectrally negative positive self-similar Markov processes. https://arxiv.org/abs/1805.04036

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