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Stochastic Fluid Models with Positive Jumps at Level Zero

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  • Hédi Nabli

    (University of Sfax)

Abstract

This paper is interested in studying a type of production models-stocks that can be seen as a stochastic fluid flow system with upward jumps at level zero. The joint distribution of the stocks level and the controlling Markov process is governed by two differential systems with specific boundary conditions. The uniqueness of the solution of this problem has been proved. Also, a unified solution with no distinction between singular or invertible drift matrix is proposed. The mathematical expectation is therefore derived. This method is based on the uniformization technique, which is acknowledged by its numerical stability and accuracy. A comparative study with a spectral-based solution is achieved to confirm this statement.

Suggested Citation

  • Hédi Nabli, 2022. "Stochastic Fluid Models with Positive Jumps at Level Zero," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 289-308, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09852-y
    DOI: 10.1007/s11009-021-09852-y
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    References listed on IDEAS

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    1. Wendi Li & Yuanyuan Liu & Yiqiang Q. Zhao, 2019. "Exact tail asymptotics for fluid models driven by an M/M/c queue," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 319-346, April.
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    Cited by:

    1. Hédi Nabli & Itidel Abdallah, 2023. "Stochastic Fluid Models with Upward Jumps and Phase Transitions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.

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