A limit theorem for Markov chains with continuous state space
نویسندگان
چکیده
منابع مشابه
On Markov Chains with Continuous State Space
In this expository paper, we p r o ve the following theorem, which m a y be of some use in studying Markov chain Monte Carlo methods like hit and run, the Metropolis algorithm, or the Gibbs sampler. Suppose a discrete-time Markov c hain is aperiodic, irreducible, and there is a stationary probability distribution. Then from almost all starting points the distribution of the chain at time n conv...
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Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, which is not necessarily reflected in similar behaviours at the level of traject...
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G. FORT1,*,∗ , E. MOULINES1,**,∗ , P. PRIOURET2,† , P. VANDEKERKHOVE3,‡ LTCI, TELECOM ParisTech & CNRS, 46 rue Barrault, 75634 Paris Cedex 13, France E-mail: [email protected]; [email protected] LPMA, Univ. Pierre et Marie Curie, Bôıte courrier 188 75252 PARIS Cedex 05, France E-mail: †[email protected] LAMA, Univ. Paris-Est Marne-la-Vallée, Cité Descarte...
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Let (S,G, P ) be a probability space and let F be a set of measurable functions on S with an envelope function F finite everywhere. Let X1, X2, ... be a strictly stationary sequence of random variables with distribution P , and define the empirical measures Pn, based on {Xi}, as Pn = n−1 ∑n i=1 δXi . We say the uniform CLT holds over F , if n 1 2 (Pn − P ) converges in law, in the space l∞(F ) ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1963
ISSN: 0004-9735
DOI: 10.1017/s1446788700028378