Invariant Measures for Markov Processes

INVARIANT MEASURES FOR MARKOV PROCESSES(i)

Convergence of Invariant Measures of Truncation Approximations to Markov Processes

Let Q be the Q-matrixof an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Twoconditions guaranteeing such convergence include exponential ergodicity and stochastic monoton...

Srb Measures for Certain Markov Processes

We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval with common fixed points at 0 and 1. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then theorems are given to analyze properties of the ergodic invariant measures δ0 and δ1. In particular, sufficien...

Discrete Time Scale Invariant Markov Processes

In this paper we consider a discrete scale invariant Markov process {X(t), t ∈ R} with scale l > 1. We consider to have some fix number of observations in every scale, say T , and to get our samples at discrete points α, k ∈ W, where α is obtained by the equality l = α and W = {0, 1, . . .}. So we provide a discrete time scale invariant Markov (DT-SIM) process X(·) with parameter space {α, k ∈ ...

Drift conditions and invariant measures for Markov chains

We consider the classical Foster–Lyapunov condition for the existence of an invariant measure for a Markov chain when there are no continuity or irreducibility assumptions. Provided a weak uniform countable additivity condition is satis/ed, we show that there are a /nite number of orthogonal invariant measures under the usual drift criterion, and give conditions under which the invariant measur...