Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5130044 | Stochastic Processes and their Applications | 2017 | 26 Pages |
Abstract
For a wide class of continuous-time Markov processes evolving on an open, connected subset of Rd, the following are shown to be equivalent: (i)The process satisfies (a slightly weaker version of) the classical Donsker-Varadhan conditions;(ii)The transition semigroup of the process can be approximated by a finite-state hidden Markov model, in a strong sense in terms of an associated operator norm;(iii)The resolvent kernel of the process is 'v-separable', that is, it can be approximated arbitrarily well in operator norm by finite-rank kernels. Under any (hence all) of the above conditions, the Markov process is shown to have a purely discrete spectrum on a naturally associated weighted Lâ space.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
I. Kontoyiannis, S.P. Meyn,