Eigentime identity for transient Markov chains

Cheeger inequalities for transient Markov chains

We construct upper and lower bounds for Cheeger-type constants for transient Markov chains. We first treat the situation where there is a detailed balance condition and obtain bounds that rely exclusively on the first and second eigenvalues of the substochastic transition matrix. Secondly, we consider general substochastic transition matrices and develop bounds in this broader setting. The effi...

Transient Markov Chains with Stationary Measures

Taylor Expansion for the Entropy Rate of Hidden Markov Chains

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

Simulation of transient performance measures for stiff markov chains

We consider the simulation of transient performance measures of high reliable faulttolerant computer Systems. The most widely used mathematical tools to model the behavior of these Systems are Markov processes. Here, we deal basically with the simulation ofthe mean time tofailure (MTTF) and the reliability, R(t), ofthe system at time t Some variance réduction techniques are used to reduce the s...

Stiffness-tolerant Methods for Transient Analysis of Stiff Markov Chains

-Three methods for numerical transient analysis of Markov chains, the modified Jensen's method (Jensen's method with steady-state detection of the underlying DTMC and computation of Poisson probabilities using the method of Fox and Glynn [1]), a third-order L-stable implicit Runge-Kutta method, and a second-order L-stable method, TR-BDF2, are compared. These methods are evaluated on the basis o...