Law of the absorption time of some positive self-similar Markov processes
By Pierre Patie. 2009
51 citations recorded by the source corpus.
Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We provide a power series and a contour integral representation of this density. Then, by means of probabilistic arguments, we deduce some interesting analytical properties satisfied by these functions, which include, for instance, several types of hypergeometric functions. We also give several characterizations of the Kesten’s constant appearing in the study of the asymptotic tail distribution of the absorbtion time. We end the paper by detailing some known and new examples. In particular, we offer an alternative proof of the recent result obtained by Bernyk, Dalang and Peskir [Ann. Probab. 36 (2008) 1777–1789] regarding the law of the maximum of spectrally positive Levy stable processes.
Subfields: Finance, Management Information Systems, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/96c6bf5895c6d6acf3037f21d09fd23daef7858c
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Citations in the corpus
- Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes (2010, unknown): “Cramér condition (see for instance [40]).”
- Bernstein-gamma functions and exponential functionals of Levy Processes (2016, methodology): “The latter for example immediately recovers the asymptotic behaviour of the density of the supremum of a stable Lévy process as investigated in [8, 25, 40, 56].”