A functional limit theorem for a 2d random walk with dependent marginals
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A functional limit theorem for a 2d-random walk with dependent marginals Nadine Guillotin-Plantard?, Arnaud Le Ny† May 21, 2007 Abstract We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent. AMS 2000 subject classification: Primary- 60F17 ; secondary- 60G18, 60K37. Keywords and phrases: Random walks, random environments, random sceneries, oriented lattices, functional limit theorems, self-similar and non-Gaussian processes. ?Universite Claude Bernard - Lyon I, institut Camille Jordan, batiment Braconnier, 43 avenue du 11 novem- bre 1918, 69622 Villeurbanne Cedex, France. E-mail: †Universite de Paris-Sud, laboratoire de mathematiques, batiment 425, 91405 Orsay cedex, France. E-mail: 1
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- local time
- limit theorem
- almost any
- process
- lemma has
- generalized random
- distribution when
- standard brownian
A functional limit theorem for a 2d-random walk with dependent marginals Nadine Guillotin-Plantard ∗ , Arnaud Le Ny † May 21, 2007
Abstract We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent.
AMS 2000 subject classification : Primary- 60F17 ; secondary- 60G18, 60K37. Keywords and phrases : Random walks, random environments, random sceneries, oriented lattices, functional limit theorems, self-similar and non-Gaussian processes.
∗ Universit´eClaudeBernard-LyonI,institutCamilleJordan,baˆtimentBraconnier,43avenuedu11novem-bre 1918, 69622 Villeurbanne Cedex, France. E-mail: nadine.guillotin@univ-lyon1.fr † Universit´edeParis-Sud,laboratoiredemathe´matiques,baˆtiment425,91405Orsaycedex,France.E-mail: arnaud.leny@math.u-psud.fr 1
