分段确定性马尔可夫过程的有限差分方法
A finite difference method for piecewise deterministic Markov processes
AI总结：
本文在分段确定性马尔可夫过程框架下扩展随机电报信号驱动的过程，建立刘维尔-主方程，用迎风法数值求解分布函数，证明CFL条件下的收敛性与非递减性，并给出数值测试。
摘要：
在“分段确定性马尔可夫过程”[Davis]的框架下，引入了由随机电报信号驱动的非确定性过程的扩展，涵盖更广泛的随机系统类别。建立了相应的刘维尔-主方程，并应用迎风方法对分布函数进行数值计算。在适当的Courant-Friedrichs-Lewy条件下，证明了数值解的收敛性。同一条件保持了所计算分布函数的非递减性质。给出了一些数值测试。
英文摘要：
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding Liouville-Master Equation is established and the upwind method is applied to numerical calculation of the distribution function. The convergence of the numerical solution is proved under an appropriate Courant-Friedrichs-Lewy condition. The same condition preserve the non-decreasing property of the calculated distribution function. Some numerical tests are presented.
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