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

journal contribution
posted on 2023-05-16, 23:23 authored by Bean, NG, Malgorzata O'ReillyMalgorzata O'Reilly, Taylor, PG
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.

History

Publication title

Methodology and Computing in Applied Probablility

Volume

10

Pagination

381-408

ISSN

1387-5841

Department/School

School of Natural Sciences

Publisher

Springer

Place of publication

Dordrecht, Netherlands

Rights statement

The original publication is available at www.springerlink.com

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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