Approximating a diffusion by a finite-state hidden Markov model
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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Authors
Kontoyiannis, Ioannis https://orcid.org/0000-0001-7242-6375
Meyn, SP
Abstract
© 2016 Elsevier B.V. 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 L∞space.
Description
Keywords
Markov process, Hidden Markov model, Hypoelliptic diffusion, Stochastic Lyapunov function, Discrete spectrum
Journal Title
Stochastic Processes and their Applications
Conference Name
Journal ISSN
0304-4149
1879-209X
1879-209X
Volume Title
127
Publisher
Elsevier BV