Main Content

Markov Chain Model

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.


expand all

dtmcCreate discrete-time Markov chain
mcmixCreate random Markov chain with specified mixing structure
asymptoticsDetermine Markov chain asymptotics
isergodicCheck Markov chain for ergodicity
isreducibleCheck Markov chain for reducibility
classifyClassify Markov chain states
lazyAdjust Markov chain state inertia
subchainExtract Markov subchain
hitprobCompute Markov chain hitting probabilities
hittimeCompute Markov chain hitting times
redistributeCompute Markov chain redistributions
simulateSimulate Markov chain state walks
distplotPlot Markov chain redistributions
eigplotPlot Markov chain eigenvalues
graphplotPlot Markov chain directed graph
simplotPlot Markov chain simulations


Discrete-Time Markov Chains

Markov chains are discrete-state Markov processes described by a right-stochastic transition matrix and represented by a directed graph.

Markov Chain Modeling

The dtmc class provides basic tools for modeling and analysis of discrete-time Markov chains. The class supports chains with a finite number of states that evolve in discrete time with a time-homogeneous transition structure.

Create and Modify Markov Chain Model Objects

Create a Markov chain model object from a state transition matrix of probabilities or observed counts, and create a random Markov chain with a specified structure.

Visualize Markov Chain Structure and Evolution

Visualize the structure and evolution of a Markov chain model by using dtmc plotting functions.

Work with State Transitions

This example shows how to work with transition data from an empirical array of state counts, and create a discrete-time Markov chain (dtmc) model characterizing state transitions.

Determine Asymptotic Behavior of Markov Chain

Compute the stationary distribution of a Markov chain, estimate its mixing time, and determine whether the chain is ergodic and reducible.

Compare Markov Chain Mixing Times

Compare the estimated mixing times of several Markov chains with different structures.

Identify Classes in Markov Chain

Programmatically and visually identify classes in a Markov chain.

Simulate Random Walks Through Markov Chain

Generate and visualize random walks through a Markov chain.

Compute State Distribution of Markov Chain at Each Time Step

Compute and visualize state redistributions, which show the evolution of the deterministic state distributions over time from an initial distribution.