Approximating a diffusion by a finite-state hidden Markov model
Stochastic Processes and their Applications
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Kontoyiannis, I., & Meyn, S. (2017). Approximating a diffusion by a finite-state hidden Markov model. Stochastic Processes and their Applications, 127 (8), 2482-2507. https://doi.org/10.1016/j.spa.2016.11.004
© 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.
External DOI: https://doi.org/10.1016/j.spa.2016.11.004
This record's URL: https://www.repository.cam.ac.uk/handle/1810/286768