A simple construction of the fractional Brownian motion
Copyright policy )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 different models for both cases ${1\over2}\leq H<1$ and $0
15 pages, 3 figures
- Sorbonne Paris Cité France
- Paris 13 University France
- University of Paris France
- University of Paris France
- UNIVERSITE PARIS 6 France
Random environment, Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Functional limit theorems; invariance principles, Applied Mathematics, correlated random walks, Probability (math.PR), Fractional processes, including fractional Brownian motion, Gaussian processes, Fractional Brownian motion, Modelling and Simulation, 60F17, 60G15, 60G17, 60K37, FOS: Mathematics, Processes in random environments, Correlated random walks, Mathematics - Probability
Random environment, Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Functional limit theorems; invariance principles, Applied Mathematics, correlated random walks, Probability (math.PR), Fractional processes, including fractional Brownian motion, Gaussian processes, Fractional Brownian motion, Modelling and Simulation, 60F17, 60G15, 60G17, 60K37, FOS: Mathematics, Processes in random environments, Correlated random walks, Mathematics - Probability
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