# Markov Chain Models

Discrete state-space processes characterized by transition matrices

A discrete state-space Markov process, or Markov chain, is represented by a directed graph and described by a right-stochastic transition matrix P. The distribution of states at time t + 1 is the distribution of states at time t multiplied by P. The structure of P determines the evolutionary trajectory of the chain, including asymptotics.

For an overview of the Markov chain analysis tools, see Markov Chain Modeling.

## Functions

expand all

 `dtmc` Create discrete-time Markov chain `mcmix` Create random Markov chain with specified mixing structure
 `asymptotics` Determine Markov chain asymptotics `isergodic` Check Markov chain for ergodicity `isreducible` Check Markov chain for reducibility `classify` Classify Markov chain states `lazy` Adjust Markov chain state inertia `subchain` Extract Markov subchain
 `hitprob` Compute Markov chain hitting probabilities `hittime` Compute Markov chain hitting times `redistribute` Compute Markov chain redistributions `simulate` Simulate Markov chain state walks
 `distplot` Plot Markov chain redistributions `eigplot` Plot Markov chain eigenvalues `graphplot` Plot Markov chain directed graph `simplot` Plot Markov chain simulations