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Hitting probabilities and hitting times for stochastic fluid flows

Citation

Bean, NG and O'Reilly, MM and Taylor, PG, Hitting probabilities and hitting times for stochastic fluid flows, Stochastic Processes and their Applications, 115, (9) pp. 1530-1556. ISSN 0304-4149 (2005) [Refereed Article]

DOI: doi:10.1016/j.spa.2005.04.002

Abstract

Recently 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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Stochastic Analysis and Modelling
Objective Division:Information and Communication Services
Objective Group:Communication Networks and Services
Objective Field:Mobile Data Networks and Services
Author:O'Reilly, MM (Dr Malgorzata O'Reilly)
ID Code:35532
Year Published:2005
Web of Science® Times Cited:32
Deposited By:Mathematics
Deposited On:2005-08-18
Last Modified:2011-11-28
Downloads:0

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