Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations
Joint Authors
Baumann, Hendrik
Hanschke, Thomas
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-01-13
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In a previous paper, we have shown that forward use of the steady-state difference equations arising from homogeneous discrete-state space Markov chains may be subject to inherent numerical instability.
More precisely, we have proven that, under some appropriate assumptions on the transition probability matrix P, the solution space S of the difference equation may be partitioned into two subspaces S=S1⊕S2, where the stationary measure of P is an element of S1, and all solutions in S1 are asymptotically dominated by the solutions corresponding to S2.
In this paper, we discuss the analogous problem of computing hitting probabilities of Markov chains, which is affected by the same numerical phenomenon.
In addition, we have to fulfill a somewhat complicated side condition which essentially differs from those conditions one is usually confronted with when solving initial and boundary value problems.
To extract the desired solution, an efficient and numerically stable generalized-continued-fraction-based algorithm is developed.
American Psychological Association (APA)
Baumann, Hendrik& Hanschke, Thomas. 2020. Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1174615
Modern Language Association (MLA)
Baumann, Hendrik& Hanschke, Thomas. Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations. Journal of Applied Mathematics No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1174615
American Medical Association (AMA)
Baumann, Hendrik& Hanschke, Thomas. Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1174615
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174615