1 results
A temporal factorization at the maximum for certain positive self-similar Markov processes
- Part of
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- Journal:
- Journal of Applied Probability / Volume 57 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 23 November 2020, pp. 1045-1069
- Print publication:
- December 2020
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- Article
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For a spectrally negative self-similar Markov process on
$[0,\infty)$ 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 this 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 existing results in the literature.
