On the absorption probabilities and mean time for absorption for discrete Markov chains
-
Nikolaos Halidias
Abstract
In this note we study the probability and the
mean time for absorption for discrete time Markov chains. In particular, we are
interested in estimating the mean time for absorption when
absorption is not certain and connect it with some other known
results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets
References
[1] J. Kemeny and J. Snell, Finite Markov Chains, Springer, Berlin, 1974. Search in Google Scholar
[2] T. Sheskin, Conditional mean first passage time in a Markov chain, Int. J. Manag. Sci. Eng. Manag. 8 (2013), 32–37. 10.1080/17509653.2013.783187Search in Google Scholar
[3] Y. Suhov and Mark Kelbert, Markov Chains: A Primer in Random Processes and Their Applications, Cambridge University, Cambridge, 2008. Search in Google Scholar
[4] D. Walker, The expected time until absorption when absorption is not certain, J. Appl. Probab. 35 (1998), 812–823. 10.1239/jap/1032438377Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Automatic control variates for option pricing using neural networks
- On the absorption probabilities and mean time for absorption for discrete Markov chains
- High order weak approximation for irregular functionals of time-inhomogeneous SDEs
- Optimal potential functions for the interacting particle system method
- On intersection volumes of confidence hyper-ellipsoids and two geometric Monte Carlo methods
- On a Monte Carlo scheme for some linear stochastic partial differential equations
Articles in the same Issue
- Frontmatter
- Automatic control variates for option pricing using neural networks
- On the absorption probabilities and mean time for absorption for discrete Markov chains
- High order weak approximation for irregular functionals of time-inhomogeneous SDEs
- Optimal potential functions for the interacting particle system method
- On intersection volumes of confidence hyper-ellipsoids and two geometric Monte Carlo methods
- On a Monte Carlo scheme for some linear stochastic partial differential equations
