Numerical Method for Bounds Computations of Discrete-Time Markov Chains with Different State Spaces

2009 ◽  
pp. 309-323
Author(s):  
Mourad Ahmane ◽  
Laurent Truffet
Keyword(s):  
Markov Chains ◽  
Numerical Method ◽  
Discrete Time ◽  
State Spaces

Discrete-time Markov chains

2011 ◽  
pp. 1-184
Author(s):  
Yuri Suhov ◽  
Mark Kelbert
Keyword(s):  
Markov Chains ◽  
Discrete Time

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

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 A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

scholarly journals Ruin probability with certain stationary stable claims generated by conservative flows

2007 ◽  
Vol 39 (02) ◽  
pp. 360-384 ◽  
Author(s):  
Uğur Tuncay Alparslan ◽  
Gennady Samorodnitsky
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Ruin Probability ◽  
Stable Process ◽  
Independent Interest ◽  
Stable Processes ◽  
Auxiliary Result ◽  
Initial Capital ◽  
Order Of Magnitude

We study the ruin probability where the claim sizes are modeled by a stationary ergodic symmetric α-stable process. We exploit the flow representation of such processes, and we consider the processes generated by conservative flows. We focus on two classes of conservative α-stable processes (one discrete-time and one continuous-time), and give results for the order of magnitude of the ruin probability as the initial capital goes to infinity. We also prove a solidarity property for null-recurrent Markov chains as an auxiliary result, which might be of independent interest.

Convergence of simulated annealing using Foster-Lyapunov criteria

2001 ◽  
Vol 38 (04) ◽  
pp. 975-994 ◽  
Author(s):  
Christophe Andrieu ◽  
Laird A. Breyer ◽  
Arnaud Doucet
Keyword(s):  
Simulated Annealing ◽  
Markov Chains ◽  
State Spaces ◽  
Compact Spaces ◽  
Convergence Results

Simulated annealing is a popular and much studied method for maximizing functions on finite or compact spaces. For noncompact state spaces, the method is still sound, but convergence results are scarce. We show here how to prove convergence in such cases, for Markov chains satisfying suitable drift and minorization conditions.

On nonlinear discrete-time systems driven by Markov chains

2010 ◽  
Vol 347 (5) ◽  
pp. 795-805 ◽  
Author(s):  
A. Tejada ◽  
O.R. González ◽  
W.S. Gray
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems
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