A Central Limit Theorem for Reversible Processes with Nonlinear Growth of Variance

Content Provider	Scilit
Author	Zhao, Ou Woodroofe, Michael Volný, Dalibor
Copyright Year	2010
Description	Kipnis and Varadhan (1986) showed that, for an additive functional, S n say, of a reversible Markov chain, the condition E[S n$ ^{2}$] / n → κ ∈ (0, ∞) implies the convergence of the conditional distribution of S n / √E[S n$ ^{2}$], given the starting point, to the standard normal distribution. We revisit this question under the weaker condition, E[S n$ ^{2}$] = n l(n), where l is a slowly varying function. It is shown by example that the conditional distributions of S n / √E[S n$ ^{2}$] need not converge to the standard normal distribution in this case; and sufficient conditions for convergence to a (possibly nonstandard) normal distribution are developed.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5637579C6B2D7652869BCD136679F72F/S0021900200007476a.pdf/div-class-title-a-central-limit-theorem-for-reversible-processes-with-nonlinear-growth-of-variance-div.pdf
Ending Page	1202
Page Count	8
Starting Page	1195
ISSN	00219002
e-ISSN	14756072
DOI	10.1017/s0021900200007476
Journal	Journal of applied probability
Issue Number	04
Volume Number	47
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2010-12-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Conditional Distribution Markov Chain adjoint Operator Slowly Varying Function
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty