On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance. (30th January 2018)
- Record Type:
- Journal Article
- Title:
- On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance. (30th January 2018)
- Main Title:
- On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance
- Authors:
- Longla, Martial
Peligrad, Costel
Peligrad, Magda - Abstract:
- Abstract : In this paper we study the functional central limit theorem (CLT) for stationary Markov chains with a self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n, and establish that conditional convergence in distribution of partial sums implies the functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.
- Is Part Of:
- Journal of applied probability. Volume 49:Number 4(2012)
- Journal:
- Journal of applied probability
- Issue:
- Volume 49:Number 4(2012)
- Issue Display:
- Volume 49, Issue 4 (2012)
- Year:
- 2012
- Volume:
- 49
- Issue:
- 4
- Issue Sort Value:
- 2012-0049-0004-0000
- Page Start:
- 1091
- Page End:
- 1105
- Publication Date:
- 2018-01-30
- Subjects:
- Maximal inequality, -- reversible process, -- martingale approximation, -- Markov chain, -- tightness, -- functional central limit theorem
60F17, -- 60G05, -- 60G10
519.2 - Journal URLs:
- https://www.cambridge.org/core/journals/journal-of-applied-probability ↗
- DOI:
- 10.1239/jap/1354716659 ↗
- Languages:
- English
- ISSNs:
- 0021-9002
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 6066.xml