The entrance law of the excursion measure of the reflected process for\n some classes of L 'evy processes

2019/01/25 by Loïc Chaumont, Chaumont, Loïc, Jacek Małecki +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #46N30 #60G51 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1901.09106

openalex publication_date 2019/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide integral formulae for the Laplace transform of the entrance law of\nthe reflected excursions for symmetric L 'evy processes in terms of their\ncharacteristic exponent. For subordinate Brownian motions and stable processes\nwe express the density of the entrance law in terms of the generalized\neigenfunctions for the semigroup of the process killed when exiting the\npositive half-line. We use the formulae to study in-depth properties of the\ndensity of the entrance law such as asymptotic behavior of its derivatives in\ntime variable.\n

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