The Annals of Probability

Stochastic Calculus with Respect to Gaussian Processes

Elisa ,1 2 and Alòs, Olivier Mazet, and David Nualart

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In this paper we develop a stochastic calculus with respect to a Gaussian process of the form $B_t = \int^t_0 K(t, s)\, dW_s$, where $W$ is a Wiener process and $K(t, s)$ is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums.The particular case of the fractional Brownian motion is discussed.

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Ann. Probab. Volume 29, Number 2 (2001), 766-801.

First available in Project Euclid: 21 December 2001

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Zentralblatt MATH identifier

Primary: 60N05 60H07: Stochastic calculus of variations and the Malliavin calculus

Stochastic integral Malliavin calculus Ito's formula fractional Brownian motion


Alòs, Elisa ,1 2; and Mazet, Olivier; Nualart, David. Stochastic Calculus with Respect to Gaussian Processes. Ann. Probab. 29 (2001), no. 2, 766--801. doi:10.1214/aop/1008956692.

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