A central limit theorem for random walks in random labyrinths
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Carol Bezuidenhout, Geoffrey Grimmett (1999)
Annales de l'I.H.P. Probabilités et statistiques
Rodolphe Garbit (2011)
Bulletin de la Société Mathématique de France
We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.
Bercu, Bernard, Del Moral, Pierre, Doucet, Arnaud (2009)
Electronic Journal of Probability [electronic only]
H. Walk (1980)
Journal für die reine und angewandte Mathematik
Barbour, Andrew D., Janson, Svante (2009)
Electronic Journal of Probability [electronic only]
Ion Grama, Michael Nussbaum (2002)
Annales de l'I.H.P. Probabilités et statistiques
Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)
Electronic Communications in Probability [electronic only]
Zemlys, Vaidotas (2008)
Electronic Journal of Probability [electronic only]
Vysotskiĭ, V.V. (2005)
Journal of Mathematical Sciences (New York)
A. Laurinčikas (1990)
Acta Arithmetica
Jakubowski, Adam (1997)
Electronic Journal of Probability [electronic only]
M. Denker, C. Grillenberger, G. Keller (1985)
Metrika
Huang, Wei, Zhang, Li-Xin (2007)
Electronic Communications in Probability [electronic only]
Jérôme Dedecker, Florence Merlevède, Magda Peligrad (2014)
Annales de l'I.H.P. Probabilités et statistiques
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
Guang-hui Cai (2011)
Czechoslovak Mathematical Journal
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite th moment and the covariance coefficient exponentially decreases to . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
David M. Mason (1988)
Annales de l'I.H.P. Probabilités et statistiques
Alvarez-Andrade, Sergio (2003)
Revista Colombiana de Matemáticas
Firas Rassoul-Agha, Timo Seppäläinen (2009)
Annales de l'I.H.P. Probabilités et statistiques
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Khurelbaatar Gonchigdanzan (2010)
ESAIM: Probability and Statistics
We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.
Túri, J. (2002)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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