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.

本文对研究一种生产模型感兴趣，它们可以看作是一种随机流体流动系统，其零级向上跳跃。库存水平和控制马尔可夫过程的联合分布由两个具有特定边界条件的差分系统控制。已经证明该问题的解决方案的唯一性。另外，提出了在奇异或可逆漂移矩阵之间没有区别的统一解决方案。因此得出数学期望。该方法基于均匀化技术，其数值稳定性和准确性得到认可。通过基于光谱的解决方案进行了比较研究，证实了这一说法。