Exit problems for positive self-similar Markov processes with one-sided jumps. (English) Zbl 1498.60176
Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités LI. Cham: Springer. Lect. Notes Math. 2301, 91-115 (2022).
Summary: A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided Lévy processes that underly the pssMp through the Lamperti transform. This theory is then brought to bear on solving the spatio-temporal: (i) two-sided exit problem; (ii) joint first passage problem for the pssMp and its multiplicative drawdown (resp. drawup) in the spectrally negative (resp. positive) case.
For the entire collection see [Zbl 1490.60007].
For the entire collection see [Zbl 1490.60007].
MSC:
| 60G51 | Processes with independent increments; Lévy processes |
| 60G18 | Self-similar stochastic processes |
| 60G44 | Martingales with continuous parameter |
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