Struct MarkovChain 

pub struct MarkovChain {
    pub states: usize,
    pub transition: Vec<Vec<f64>>,
}

Discrete-time Markov chain with a finite state space.

Fields

states: usize

Number of states.

transition: Vec<Vec<f64>>

Row-stochastic transition matrix: transition[i][j] = P(X_{n+1}=j | X_n=i).

Implementations

impl MarkovChain

pub fn new(transition: Vec<Vec<f64>>) -> Self

Create from a transition matrix. Rows must sum to 1.

pub fn random(states: usize, rng: &mut Rng) -> Self

Create a random transition matrix.

pub fn is_stochastic(&self) -> bool

Validate that this is a proper stochastic matrix.

pub fn step(&self, rng: &mut Rng, current_state: usize) -> usize

Single step: sample next state from current.

pub fn simulate( &self, rng: &mut Rng, initial: usize, steps: usize, ) -> Vec<usize>

Simulate a trajectory of steps states starting from initial.

pub fn stationary_distribution(&self) -> Vec<f64>

Compute stationary distribution via power iteration. Finds pi such that pi * P = pi.

pub fn is_irreducible(&self) -> bool

Check if the chain is irreducible (all states reachable from all states).

pub fn is_ergodic(&self) -> bool

Check if the chain is ergodic (irreducible and aperiodic). Aperiodicity is checked by verifying gcd of return times = 1, which we approximate by checking if P^n has all positive entries for some n.

pub fn absorbing_states(&self) -> Vec<usize>

Find absorbing states (states i where P(i,i) = 1).

pub fn mean_first_passage(&self, from: usize, to: usize) -> f64

Mean first passage time from state from to state to. Computed by solving the system: m_i = 1 + sum_{j != to} P(i,j) * m_j using iterative method.

pub fn power(&self, n: usize) -> Vec<Vec<f64>>

Compute the n-step transition matrix P^n.

pub fn empirical_stationary(&self, rng: &mut Rng, steps: usize) -> Vec<f64>

Empirical stationary distribution from a long simulation.