A classification of a random walk defined on a finite Markov chain

1973 ◽  
Vol 26 (2) ◽  
pp. 95-104 ◽  
Author(s):  
M. Newbould
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Finite Markov Chain

Some duality results for a class of multivariate semi-markov processes

1982 ◽  
Vol 19 (01) ◽  
pp. 90-98
Author(s):  
J. Janssen ◽  
J. M. Reinhard
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Processes ◽  
Queueing Theory ◽  
Random Variables ◽  
Classical Case ◽  
Risk Theory ◽  
Finite Markov Chain ◽  
Duality Results ◽  
Semi Markov Processes

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.

Some duality results for a class of multivariate semi-markov processes

1982 ◽  
Vol 19 (1) ◽  
pp. 90-98 ◽  
Author(s):  
J. Janssen ◽  
J. M. Reinhard
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Processes ◽  
Queueing Theory ◽  
Random Variables ◽  
Classical Case ◽  
Risk Theory ◽  
Finite Markov Chain ◽  
Duality Results ◽  
Semi Markov Processes

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.

scholarly journals Return Time Probability Distribution of a Finite Markov Chain

2019 ◽  
Vol 9 (1) ◽  
pp. 2520-2522
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Time Distribution ◽  
Return Time ◽  
Vital Role ◽  
Recurrence Time ◽  
Finite Markov Chain ◽  
The Mean ◽  
Discrete Markov Chain

In this paper we have considered a finite discrete Markov chain and derived a recurrence relation for the calculating the return time probability distribution. The mean recurrence time is also calculated. Return time distribution helps to identify the most frequently visited states. Return time distribution plays a vital role in the classification of Markov chain. These concepts are illustrated through an example.

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 the age distribution of a Markov chain

1978 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A(j), is the weak limit of the time given Xn = j (n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A (J) (J → ∞) are given for these examples.

scholarly journals Limit theorems for some continuous-time random walks

2011 ◽  
Vol 43 (3) ◽  
pp. 782-813 ◽  
Author(s):  
M. Jara ◽  
T. Komorowski
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Transport ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transport Theory ◽  
Sufficient Conditions ◽  
Continuous Time Random Walks ◽  
Quantum Transport Theory

In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {Xn,n≥ 0} and two observables, τ(∙) andV(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and Scheffler (2004) and Meerschaert and Scheffler (2008), and the recent results of Henry and Straka (2011) and Jurlewicz, Kern, Meerschaert and Scheffler (2010), where {Xn,n≥ 0} is a sequence of independent and identically distributed random variables.

scholarly journals One dimensional quantum walks with memory

2010 ◽  
Vol 10 (5&6) ◽  
pp. 509-524
Author(s):  
M. Mc Gettrick
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Walks ◽  
One Dimensional ◽  
With Memory ◽  
Previous Step

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of one previous step. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

Sign in / Sign up

Export Citation Format

Share Document