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Un principe d'invariance pour une classe de marches p-corrélées sur ℤd

Part of: Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Alexis Bienvenüe
Alexis Bienvenüe*
Affiliation:
Université Lyon I
*
∗Postal address: Laboratoire de Probabilités, Université Claude Bernard Lyon I, Bât. 101, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France. Email address: [email protected]
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Abstract

Let ζ be a Markov chain on a finite state space D, f a function from D to ℝd, and Sn = ∑k=1nf(ζk). We prove an invariance theorem for S and derive an explicit expression of the limit covariance matrix. We give its exact value for p-reinforced random walks on ℤ2 with p = 1, 2, 3.

Keywords

Gillis walkcharacteristic functionmomentsDonsker theorem

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 557 - 565
Copyright
Copyright © Applied Probability Trust 1998 

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