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Krinik, Alan; von Bremen, Hubertus; Ventura, Ivan; Nguyen, Uyen Vietthanh; Lin, Jeremy J.; Lu, Thuy Vu Dieu; Luk, Chon In (Dave); Yeh, Jeffrey; Cervantes, Luis A.; Lyche, Samuel R.; Marian, Brittney A.; Aljashamy, Saif A.; Dela, Mark; Oudich, Ali; Ostadhassanpanjehali, Pedram; Phey, Lyheng; Perez, David; Kath, John Joseph; Demmin, Malachi C.; Dawit, Yoseph; Hoogendyk, Christine Carmen Marie; Kim, Aaron; McDonough, Matthew; Castillo, Adam Trevor; Beecher, David; Wong, Weizhong; Ayeda, Heba

Explicit transient probabilities of various Markov models. (English) Zbl 1496.60089

Swift, Randall J. (ed.) et al., Stochastic processes and functional analysis. New perspectives. AMS special session celebrating M. M. Rao’s many mathematical contributions as he turns 90 years old. University of California, Riverside, California, November 9–10, 2019. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 774, 97-151 (2021).
Let \(P\) be the transition probability matrix corresponding to a finite-state Markov chain. The paper under review deals with finding explicit eigenvalue formulas of \(P\) and the expressions of \(P^k\) where \(k=2, 3, 4\ldots\) for various Markov chains. These results are also applied to find probabilities of sample paths restricted to a strip and generalized ballot box problems.
For the entire collection see [Zbl 1493.60004].
Reviewer: Liping Li (Beijing)

Cited in 1 Document

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J22 Computational methods in Markov chains

Keywords:

Markov chains and Markov processes; eigenvalues and eigenvectors; transient probabilities; ballot box problem; dual processes; transition probability matrix; tridiagonal matrices; Toeplitz matrices; circulant matrices; spectral projectors; gambler’s ruin; catastrophes
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Full Text: DOI

References:

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