Asymptotic solution of stochastic fluid model with upward jumps

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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. This method is based on the randomization technique, which is acknowledged by its numerical stability and accuracy. Key Words: Markov process, Partial differential equations, Stochastic fluid models.
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