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2006•Unpublished venueOpen access

Fractional Brownian motion

David Nualart

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Abstract

Abstract The fractional Brownian motion is a self-similar centered Gaussian process with stationary increments and variance equals t2H, where H is a parameter in the interval (0, 1). For H = ½ this process is a classical Brownian motion. In this chapter we will present the application of the Malliavin Calculus to develop a stochastic calculus with respect to the fractional Brownian motion.

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Abstract The fractional Brownian motion is a self-similar centered Gaussian process with stationary increments and variance equals t2H, where H is a parameter in the interval (0, 1). For H = ½ this process is a classical Brownian motion. In this chapter we will present the application of the Malliavin Calculus to develop a stochastic calculus with respect to the fractional Brownian motion.

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Available abstract

Abstract The fractional Brownian motion is a self-similar centered Gaussian process with stationary increments and variance equals t2H, where H is a parameter in the interval (0, 1). For H = ½ this process is a classical Brownian motion. In this chapter we will present the application of the Malliavin Calculus to develop a stochastic calculus with respect to the fractional Brownian motion.

Key concepts: Fractional Brownian motion, Brownian excursion, Mathematics, Reflected Brownian motion, Brownian motion, Martingale representation theorem, Diffusion process, Malliavin calculus

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