The first hitting time of the integers by symmetric Lévy processes

Yasuki Isozaki

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1782-1794

Abstract: For one-dimensional Brownian motion, the exit time from an interval has finite exponential moments and its probability density is expanded in exponential terms. In this note we establish its counterpart for certain symmetric Lévy processes. Applying the theory of Pick functions, we study properties of the Laplace transform of the first hitting time of the integer lattice as a meromorphic function in detail. Its density is expanded in exponential terms and the poles and the zeros of a Pick function play a crucial role.

Keywords: Lévy process; Probabilistic potential theory; Pick function; Fractional linear transformations (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.06.001

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