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Hitting probabilities and hitting times for stochastic fluid flows
journal contribution
posted on 2023-05-16, 16:54 authored by Bean, NG, Malgorzata O'ReillyMalgorzata O'Reilly, Taylor, PGRecently there has been considerable interest in Markovian stochastic fluid flow models. A number of authors have used different methods to calculate quantities of interest. In this paper, we consider a fluid flow model, formulated so that time is preserved, and derive expressions for return probabilities to the initial level, the Laplace-Stieltjes transforms (for arguments with nonnegative real part only) and moments of the time taken to return to the initial level, excursion probabilities to high/low levels, and the Laplace-Stieltjes transforms of sojourn times in specified sets. An important feature of our results is their physical interpretation within the stochastic fluid flow environment, which is given. This allows for further implementation of our expressions in the calculation of other quantities of interest.
History
Publication title
Stochastic Processes and their ApplicationsVolume
115Issue
9Pagination
1530-1556ISSN
0304-4149Department/School
School of Natural SciencesPublisher
Elsevier Science BVPlace of publication
AMSTERDAM, NETHERLANDS, 1000 AERepository Status
- Restricted