An Estimate for the Convergence Rate in a Renewal Theorem for Random Variables Defined on a Markov Chain

1973 ◽  
Vol 17 (3) ◽  
pp. 535-543
Author(s):  
A. E. Zaslavskii
Keyword(s):  
Markov Chain ◽  
Convergence Rate ◽  
Random Variables ◽  
Renewal Theorem

Infinite dams with inputs forming a Markov chain

1968 ◽  
Vol 5 (1) ◽  
pp. 72-83 ◽  
Author(s):  
M. S. Ali Khan ◽  
J. Gani
Keyword(s):  
Markov Chain ◽  
Storage Systems ◽  
Random Variables ◽  
Time Intervals ◽  
Storage Theory ◽  
Annual Time ◽  
Theory Of Storage ◽  
Independent And Identically Distributed

Moran's [1] early investigations into the theory of storage systems began in 1954 with a paper on finite dams; the inputs flowing into these during consecutive annual time-intervals were assumed to form a sequence of independent and identically distributed random variables. Until 1963, storage theory concentrated essentially on an examination of dams, both finite and infinite, fed by inputs (discrete or continuous) which were additive. For reviews of the literature in this field up to 1963, the reader is referred to Gani [2] and Prabhu [3].

The Study on Convergence and Convergence Rate of Genetic Algorithm Based on an Absorbing Markov Chain

2012 ◽  
Vol 239-240 ◽  
pp. 1511-1515 ◽  
Author(s):  
Jing Jiang ◽  
Li Dong Meng ◽  
Xiu Mei Xu
Keyword(s):  
Genetic Algorithm ◽  
Markov Chain ◽  
Convergence Rate ◽  
Hitting Time ◽  
Sufficient Condition ◽  
First Hitting Time ◽  
Absorbing Markov Chain ◽  
Expected Hitting Time ◽  
Optimization Efficiency ◽  
Theoretical Issues

The study on convergence of GA is always one of the most important theoretical issues. This paper analyses the sufficient condition which guarantees the convergence of GA. Via analyzing the convergence rate of GA, the average computational complexity can be implied and the optimization efficiency of GA can be judged. This paper proposes the approach to calculating the first expected hitting time and analyzes the bounds of the first hitting time of concrete GA using the proposed approach.

Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

1987 ◽  
Vol 24 (02) ◽  
pp. 347-354 ◽  
Author(s):  
Guy Fayolle ◽  
Rudolph Iasnogorodski
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Stochastic Processes ◽  
State Space ◽  
Discrete Time ◽  
Random Variables ◽  
Countable State Space ◽  
Countable State ◽  
New Criteria

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn ), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn ) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

scholarly journals Approximations: replacing random variables with their means

2014 ◽  
Vol 51 (A) ◽  
pp. 57-62
Author(s):  
Joe Gani
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Continuous Time ◽  
Random Variables ◽  
Original Form ◽  
Continuous Time Markov Chain ◽  
Standard Methods ◽  
Sis Epidemics

One of the standard methods for approximating a bivariate continuous-time Markov chain {X(t), Y(t): t ≥ 0}, which proves too difficult to solve in its original form, is to replace one of its variables by its mean, This leads to a simplified stochastic process for the remaining variable which can usually be solved, although the technique is not always optimal. In this note we consider two cases where the method is successful for carrier infections and mutating bacteria, and one case where it is somewhat less so for the SIS epidemics.

Sums and weighted sums of a gamma Markov sequence

1988 ◽  
Vol 25 (01) ◽  
pp. 204-209 ◽  
Author(s):  
Ravindra M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Random Variables ◽  
Laplace Transforms ◽  
Weighted Sums ◽  
Sums Of Random Variables ◽  
Markov Sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

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