Stochastic Fluid Models with Upward Jumps and Phase Transitions

Hédi Nabli () and Itidel Abdallah ()
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Hédi Nabli: Universty of Sfax
Itidel Abdallah: Universty of Sfax

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-26

Abstract: Abstract In this paper, we are interested in stochastic fluid flow model with upward jumps at level zero and instantaneous phase transitions at jumps epochs. This mathematical model is governed by a non-homogeneous differential system with specific boundary conditions. We derive three algorithms for computing explicitly the fluid level distribution. We study the general case of the model, the case where the phase process conserves its state when the fluid jumps, and a special case where the phase process transits to a deterministic fixed state at jumps epochs. Numerical results are carried out to illustrate the numerical stability and the advantages in computational time for the proposed approaches.

Keywords: Stochastic fluid model; Stationary distribution; Markov process; Conditioning of matrices; 60J25; 60J75; 15A18; 15A12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09982-5

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