混合状态空间上马尔可夫链演化的稳态概率计算

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-03-30 DOI:10.1515/mcma-2023-2003
Az-eddine Zakrad, A. Nasroallah
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引用次数: 0

摘要

分划算法是显式计算有限马尔可夫链稳态概率的迭代过程𝑋。在本文中,我们提出将该算法应用于状态空间E:=C∪D E:=C \cup D由连续部分和有限部分𝐷组成,使得C∩D=∅C \cap D= \emptyset。在这种情况下,稳态概率𝑋分别是两条马尔可夫链的两个稳态概率π C \pi _C{和π }D \pi _D{的凸组合。得到的算法允许显式计算π D }\pi _D{。如果π C }\pi _C{不能显式计算,我们的算法通过连续积分方程的数值解析近似它。通过数值算例分析,说明了该方法的有效性和良好的功能。}
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Computation of the steady-state probability of Markov chain evolving on a mixed state space
Abstract The partitioning algorithm is an iterative procedure that computes explicitly the steady-state probability of a finite Markov chain 𝑋. In this paper, we propose to adapt this algorithm to the case where the state space E := C ∪ D E:=C\cup D is composed of a continuous part 𝐶 and a finite part 𝐷 such that C ∩ D = ∅ C\cap D=\emptyset . In this case, the steady-state probability 𝜋 of 𝑋 is a convex combination of two steady-state probabilities π C \pi_{C} and π D \pi_{D} of two Markov chains on 𝐶 and 𝐷 respectively. The obtained algorithm allows to compute explicitly π D \pi_{D} . If π C \pi_{C} cannot be computed explicitly, our algorithm approximates it by numerical resolution of successive integral equations. Some numerical examples are studied to show the usefulness and proper functioning of our proposal.
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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