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April 2001 Stochastic Calculus with Respect to Gaussian Processes
Elisa Alòs, Olivier Mazet, David Nualart
Ann. Probab. 29(2): 766-801 (April 2001). DOI: 10.1214/aop/1008956692

Abstract

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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Elisa Alòs. Olivier Mazet. David Nualart. "Stochastic Calculus with Respect to Gaussian Processes." Ann. Probab. 29 (2) 766 - 801, April 2001. https://doi.org/10.1214/aop/1008956692

Information

Published: April 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1015.60047
MathSciNet: MR1849177
Digital Object Identifier: 10.1214/aop/1008956692

Subjects:
Primary: 60H07 , 60N05

Keywords: fractional Brownian motion , Ito's formula , Malliavin calculus , stochastic integral

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 2 • April 2001
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