A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations

• Published in: SIAM journal on numerical analysis Vol. 37; no. 4; pp. 1120 - 1137
• Main Authors: Shardlow, T., Stuart, A. M.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2000
• Subjects: Applied mathematics; Approximation; Banach spaces; Computational mathematics; Differential equations; Ergodic theory; Exact sciences and technology; Integers; Markov analysis; Markov chains; Markov processes; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Noise; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods; Ordinary differential equations; Perturbation theory; Probability and statistics; Probability theory and stochastic processes; Random variables; Sciences and techniques of general use; Spacetime; Stochastic analysis; Markov process; Ergodic theory; Brownian noise; Exponential distribution; Differential equation; Stochastic partial differential equation; Perturbation; Euler scheme; Partial differential equation; Truncation error; Numerical approximation; Markov chain; Brownian motion; Parabolic equation; Sigma algebra; Impulse; Stochastic equation; Stochastic differential equation

Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster-Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time inter...