Markov chains and tensor multiplications

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Markov chains

[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

Markov Chains and Applications

In this paper I provide a quick overview of Stochastic processes and then quickly delve into a discussion of Markov Chains. There is some assumed knowledge of basic calculus, probability, and matrix theory. I build up Markov Chain theory towards a limit theorem. I prove the Fundamental Theorem of Markov Chains relating the stationary distribution to the limiting distribution. I then employ this...

Markov and the Creation of Markov Chains

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 ...