A simple construction of the fractional Brownian motion

A simple construction of the fractional Brownian motion

In this work we introduce correlated random walks on Z . When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is the fractional Brownian motion. We have to use two radically dif...

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Veröffentlicht in:Stochastic processes and their applications 2004-02, Vol.109 (2), p.203-223
1. Verfasser: Enriquez, Nathanaël
Format: Artikel
Sprache:eng
Schlagworte:
Correlated random walks
Correlated random walks Random environment Fractional Brownian motion
Exact sciences and technology
Fractional Brownian motion
Limit theorems
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Random environment
Sciences and techniques of general use
Stochastic analysis
Stochastic processes
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Zusammenfassung:In this work we introduce correlated random walks on Z . When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is the fractional Brownian motion. We have to use two radically different models for both cases 1 2 ⩽H
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2003.10.008