# Multifractional Brownian Motion : Definition and Preliminary Results

Abstract : We generalize the definition of the fractional Brownian motion of exponent $H$ to the case where $H$ is no longer a constant, but a function of the time index of the process. This allows us to model non stationary continuous processes, and we show that $H(t)$ and $2-H(t)$ are indeed respectively the local Hölder exponent and the local box and Hausdorff dimension at point $t$. Finally, we propose a simulation method and an estimation procedure for $H(t)$ for our model.
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https://hal.inria.fr/inria-00074045
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Submitted on : Wednesday, May 24, 2006 - 2:22:46 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
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### Identifiers

• HAL Id : inria-00074045, version 1

### Citation

Romain-François Peltier, Jacques Lévy Véhel. Multifractional Brownian Motion : Definition and Preliminary Results. [Research Report] RR-2645, INRIA. 1995. ⟨inria-00074045⟩

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