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Journal Articles Methodology and Computing in Applied Probability Year : 2023

Stochastic Fluid Models with Upward Jumps and Phase Transitions

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.
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Dates and versions

hal-04356025 , version 1 (20-12-2023)

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Hédi Nabli, Itidel Abdallah. Stochastic Fluid Models with Upward Jumps and Phase Transitions. Methodology and Computing in Applied Probability, 2023, 25 (1), pp.7. ⟨10.1007/s11009-023-09982-5⟩. ⟨hal-04356025⟩
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