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Type: Journal article
Title: Algorithms for the Laplace–Stieltjes transforms of first return times for stochastic fluid flows
Author: Bean, N.
O'Reilly, M.
Taylor, P.
Citation: Methodology and Computing in Applied Probability, 2008; 10(3):381-408
Publisher: Kluwer Academic Publishers
Issue Date: 2008
ISSN: 1387-5841
Statement of
Nigel G. Bean, Małgorzata M. O’Reilly and Peter G. Taylor
Abstract: 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.
Keywords: Markovian fluid model
Ricatti equation
Newton’s method
reduction algorithm
Cyclic-reduction algorithm
DOI: 10.1007/s11009-008-9077-3
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