Central limit theorems for additive functionals of Markov chains

By M. Maxwell, Michael Woodroofe. 2000

241 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ac2ce70f3801fa34ca119ba0398825658536dcbe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Magda Peligrad
2. Wei Biao Wu
3. F. Merlevède
4. C. Cuny
5. Sergey Utev
6. Y. Derriennic
7. Michael Lin
8. Zemer Kosloff

In Statistics and Probability

1. C. Cuny
2. Magda Peligrad
3. Sergey Utev
4. F. Merlevède
5. Marek Tomasz Biskup
6. Wei Biao Wu
7. Y. Derriennic
8. Michael Lin

Citations in the corpus

• Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “Starting with the binary expansion (22), and using Minkowski’s inequality twice, first with respect to the conditional expectation, and second with respect to the norm in L, we get by stationarity that ‖E0(S(2) n)‖p/2 ≤ ( r−1 ∑”
• Martingale–coboundary decomposition for families of dynamical systems (2016, methodology): “One of the standard techniques for investigating such phenomena is the martingalecoboundary decomposition method of Gordin [26] which has seen extensive development in both the probability theory literature (for example [31, 35, 41, 51]) and in the dynamical systems literature (for example [39, 54, ”
• An invariance principle for stationary random fields under Hannan's condition (2014, background): “Indeed, they constructed a counterexample to show that Hannan’s condition does not imply the Maxwell–Woodroofe condition [18], and the latter is known to be strictly weaker than (6.”
• Central limit theorem for stationary linear processes (2005, methodology): “The following result extends Proposition 3 in [17] in the context of Bernoulli shifts (also called Raikov or Riesz–Raikov sums) and follows as an application of Corollary 2.”
• The central limit theorem for Markov chains started at a point (2003, methodology): “In another recent paper [ MW ], which appeared after the paper [DL3] has been sent to the press, Maxwell and Woodroofe proved the convergence in distribution of n −”
• Recent advances in invariance principles for stationary sequences (2006, methodology): “Maxwell and Woodroofe [35] have specialized their central limit theorem and invariance principle to one-sided shift processes, also known under the name of Raikov sums.”
• Central limit theorem for Markov processes with spectral gap in the Wasserstein metric (2011, background): “[8, 27, 35] and in [21] for continuous time processes.”
• Asymptotic theory for stationary processes (2011, background): “Hoeffding (1961), O’Neil and Redner (1993), Major (1994) and Rifi and Utzet (2000) considered properties of Un for iid observations.”
• Pointwise ergodic theorems with rate and application to limit theorems for stationary processes (2009, methodology): “They worked with Markov chains with symmetric Markov operator, but the method applies in general, as it was done by MaxwellWoodroofe [14].”
• Recent progress on the Random Conductance Model (2011, background): “Another approach goes by imposing decay-rate conditions on time-correlations (e.g., Maxwell and Woodroofe [103], Derriennic and Lin [47], Peligrad and Utev [113], Klicnarová and Volný [88], Volný [133], etc.).”
• Law of the iterated logarithm for stationary processes (2006, methodology): “ar X iv :m at h/ 06 12 74 7v 2 [ m at h. PR ] 1 1 D ec 2 00 7 The Annals of Probability 2008, Vol. 36, No. 1, 127–142 DOI: 10.1214/009117907000000079 c© Institute of Mathematical Statistics, 2008 LAW OF THE ITERATED LOGARITHM FOR STATIONARY PROCESSES1 By Ou Zhao and Michael Woodroofe University of M”