Time reversal and age distributions, I. Discrete-time Markov chains

1980 ◽  
Vol 17 (1) ◽  
pp. 33-46 ◽  
Author(s):  
S. Tavaré
Keyword(s):  
Population Genetics ◽  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Time Reversal ◽  
Age Distribution ◽  
Applied Probability ◽  
Discrete Time Markov Chain

The connection between the age distribution of a discrete-time Markov chain and a certain time-reversed Markov chain is exhibited. A method for finding properties of age distributions follows simply from this approach. The results, which have application in several areas in applied probability, are illustrated by examples from population genetics.

Time reversal and age distributions, I. Discrete-time Markov chains

1980 ◽  
Vol 17 (01) ◽  
pp. 33-46 ◽  
Author(s):  
S. Tavaré
Keyword(s):  
Population Genetics ◽  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Time Reversal ◽  
Age Distribution ◽  
Applied Probability ◽  
Discrete Time Markov Chain

The connection between the age distribution of a discrete-time Markov chain and a certain time-reversed Markov chain is exhibited. A method for finding properties of age distributions follows simply from this approach. The results, which have application in several areas in applied probability, are illustrated by examples from population genetics.

Lumpability for non-irreducible finite markov chains

1984 ◽  
Vol 21 (03) ◽  
pp. 567-574 ◽  
Author(s):  
Atef M. Abdel-Moneim ◽  
Frederick W. Leysieffer
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
The State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

Conditions under which a function of a finite, discrete-time Markov chain, X(t), is again Markov are given, when X(t) is not irreducible. These conditions are given in terms of an interrelationship between two partitions of the state space of X(t), the partition induced by the minimal essential classes of X(t) and the partition with respect to which lumping is to be considered.

scholarly journals Recursive smoothers for hidden discrete-time Markov chains

2005 ◽  
Vol 2005 (3) ◽  
pp. 345-351
Author(s):  
Lakhdar Aggoun
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Em Algorithm ◽  
Discrete Time ◽  
Expectation Maximization ◽  
Discrete Time Markov Chain ◽  
Proposed Model

We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995). We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM) algorithm.

scholarly journals First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Mario Lefebvre ◽  
Moussa Kounta
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Geometric Brownian Motion ◽  
Expected Number ◽  
Discrete Time Markov Chain

We consider a discrete-time Markov chain with state space {1,1+Δx,…,1+kΔx=N}. We compute explicitly the probability pj that the chain, starting from 1+jΔx, will hit N before 1, as well as the expected number dj of transitions needed to end the game. In the limit when Δx and the time Δt between the transitions decrease to zero appropriately, the Markov chain tends to a geometric Brownian motion. We show that pj and djΔt tend to the corresponding quantities for the geometric Brownian motion.

General transition probabilities for finite Markov chains

1964 ◽  
Vol 60 (1) ◽  
pp. 83-91 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Finite Number ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Initial State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

We consider a stationary discrete-time Markov chain with a finite number m of possible states which we designate by 1,…,m. We assume that at time t = 0 the process is in an initial state i with probability (i = 1,…, m) and such that and .

scholarly journals Application of a Discrete-time Markov Chain Simulation in Insurance

2015 ◽  
Vol 3 (3) ◽  
pp. 27 ◽  
Author(s):  
Antonio Fernandez-Morales
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Learning Process ◽  
Main Parameter ◽  
Perceived Usefulness ◽  
Automobile Insurance ◽  
Preliminary Assessment ◽  
Discrete Time Markov Chain ◽  
Insurance Model

This paper describes the application of an online interactive simulator of discrete-time Markov chains to an automobile insurance model. Based on the D3.js library, an interactive visual animation depicts the dynamics of individual policyholders in a bonus-malus system of automobile insurance. A survey was conducted among MSc students who used the simulator to obtain a preliminary assessment of the perceived usefulness in several dimensions of their learning process. The main findings indicate that flexible access via different devices was the most valued feature of this resource. In addition, the possibility of experimenting and simulating by means of controlling the main parameter of the model was also found to be particularly useful.

Lumpability for non-irreducible finite markov chains

1984 ◽  
Vol 21 (3) ◽  
pp. 567-574 ◽  
Author(s):  
Atef M. Abdel-Moneim ◽  
Frederick W. Leysieffer
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
The State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

Conditions under which a function of a finite, discrete-time Markov chain, X(t), is again Markov are given, when X(t) is not irreducible. These conditions are given in terms of an interrelationship between two partitions of the state space of X(t), the partition induced by the minimal essential classes of X(t) and the partition with respect to which lumping is to be considered.

scholarly journals Markovian bounds on functions of finite Markov chains

2001 ◽  
Vol 33 (2) ◽  
pp. 505-519 ◽  
Author(s):  
James Ledoux ◽  
Laurent Truffet
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coupling Method ◽  
Geometric Invariant ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains ◽  
Stochastic Majorization ◽  
Necessary And Sufficient

In this paper, we obtain Markovian bounds on a function of a homogeneous discrete time Markov chain. For deriving such bounds, we use well-known results on stochastic majorization of Markov chains and the Rogers–Pitman lumpability criterion. The proposed method of comparison between functions of Markov chains is not equivalent to generalized coupling method of Markov chains, although we obtain same kind of majorization. We derive necessary and sufficient conditions for existence of our Markovian bounds. We also discuss the choice of the geometric invariant related to the lumpability condition that we use.

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}} .

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