A sequence (X_n) on state space S satisfying the Markov property P(X_{n+1}=y | X_n=x, …) = P(X_{n+1}=y | X_n=x). Stationary distributions, ergodicity, mixing times are core topics.
Markov chain
Related concepts
- Conditional probability
- Poisson process
- Kolmogorov probability axioms
- Chapman-Kolmogorov (1931)
- Doob decomposition (1953)
- Detailed balance
- Markov chain Monte Carlo (MCMC)
- Agent-based financial models
- Opinion dynamics (Galam / Deffuant)
- Voter model (Clifford-Sudbury)
- MCMC (Metropolis 1953 / Hastings 1970)
- Persistent organic pollutants (POPs)
- Spur-track structure: LET scaling ρ_track ∝ LET; α/γ ≈ 2000/3
- s-process framework: σ·N = const along s-only path (slow neutron capture local equilibrium)
- Catalytic ozone destruction (Cl, NO, HO_x)
- Monte Carlo (Metropolis algorithm)
- Dimethyl sulfide & cloud-condensation (CLAW hypothesis)
- Metropolis Monte Carlo (1953)
- Plasmid-loss exponential decay: fraction retained = e^{−λn}; binary-fission dilution Markov chain
- Hidden Markov model (bio applications)