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Algorithms for the Laplace-Stieltjes transforms of first return times for Stochastic fluid flows


Bean, NG and O'Reilly, MM and Taylor, PG, Algorithms for the Laplace-Stieltjes transforms of first return times for Stochastic fluid flows, Methodology and Computing in Applied Probablility, 10, (3) pp. 381-408. ISSN 1387-5841 (2008) [Refereed Article]

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DOI: doi:10.1007/s11009-008-9077-3


We derive several algorithms, including quadratically convergent algorithms, which can be used to calculate the Laplace–Stieltjes transforms of the time taken to return to the initial level in the Markovian stochastic fluid flow model. We give physical interpretations of the algorithms and consider their numerical analysis. The numerical performance of the algorithms, which depends on the physical properties of the process, is discussed and illustrated with simple examples. Besides the powerful algorithms, this paper contributes interesting theoretical results. In particular, the methodology for constructing these algorithms is a valuable contribution to the theory of fluid flow models. Moreover, useful physical interpretations of the algorithms, and related expressions, given in terms of the fluid flow model, can assist in further analysis and help in a better understanding of the model.

Item Details

Item Type:Refereed Article
Keywords:Markovian fluid model, Ricatti equation, Newton's method, Logarithmic-reduction algorithm, cyclic-reduction algorithm
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Stochastic analysis and modelling
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:O'Reilly, MM (Associate Professor Malgorzata O'Reilly)
ID Code:55966
Year Published:2008
Web of Science® Times Cited:31
Deposited By:Mathematics
Deposited On:2009-03-17
Last Modified:2015-01-27

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