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Random walk, birth-and-death process and their fluid approximations: absorbing case

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  • A. Piunovskiy

Abstract

Fluid models are used to study functionals of the underlying random processes. Instead of analysing the trajectories, we investigate algebraic equations of the dynamic programming type which turn out to be discrete analogs of the corresponding differential equations. This analysis makes it possible to estimate the accuracy of approximation. Since the algebraic equations are the same for random walks and continuous time birth-and-death processes, we study the two cases in parallel. Several illustrative examples are also presented. Copyright Springer-Verlag 2009

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  • A. Piunovskiy, 2009. "Random walk, birth-and-death process and their fluid approximations: absorbing case," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 285-312, October.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:2:p:285-312
    DOI: 10.1007/s00186-008-0269-y
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    Cited by:

    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.

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