A simple construction of the Fractional Brownian motion

By E. Nathanael. 2002

48 citations recorded by the source corpus.

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 $0<H<{1\over2}$. This result provides an algorithm for the simulation of the fractional Brownian motion, which appears to be quite efficient.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/45406b1b88fce0098913f789d8ebfc288f4cd6ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Laure Coutin
2. David Nualart
3. Martin Hairer
4. Peter K. Friz
5. Bruno Saussereau

In Finance

1. Laure Coutin
2. David Nualart
3. Peter K. Friz
4. Martin Hairer
5. Antoine Lejay
6. Yaozhong Hu
7. Nicolas Victoir
8. Bruno Saussereau

Citations in the corpus

• An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion (2007, methodology): “A simple construction of fractional Brownian motion is given by Enriquez, [ Enr04 ].”