Subgeometric ergodicity for continuous-time Markov chains

Subgeometric ergodicity of Markov chains

When f ≡ 1, the f -norm is the total variation norm, which is denoted ‖μ‖TV. Assume that P is aperiodic positive Harris recurrent with stationary distribution π. Then the iterated kernels P(x, ·) converge to π. The rate of convergence of P(x, .) to π does not depend on the starting state x, but exact bounds may depend on x. Hence, it is of interest to obtain non uniform or quantitative bounds o...

Limit Theorems for subgeometric Markov chains

This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster-Lyapunov conditions. The regeneration-split chain method...

Discrete Time Markov Chains : Ergodicity Theory

Lecture 8: Discrete Time Markov Chains: Ergodicity Theory Announcements: 1. We handed out HW2 solutions and your homeworks in Friday’s recitation. I am handing out a few extras today. Please make sure you get these! 2. Remember that I now have office hours both: Wednesday at 3 p.m. and Thursday at 4 p.m. Please show up and ask questions about the lecture notes, not just the homework! No one cam...

Continuous Time Markov Chains

Discrete-time Markov chains are useful in simulation, since updating algorithms are easier to construct in discrete steps. They can also be useful as crude models of physical, biological, and social processes. However, in the physical and biological worlds time runs continuously, and so discrete-time mathematical models are not always appropriate. This is especially true in population biology –...

Continuous-time Markov Chains