Annals of Probability

Stochastic Calculus with Respect to Gaussian Processes

Elisa Alòs, Olivier Mazet, and David Nualart

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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.

Article information

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

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956692

Digital Object Identifier
doi:10.1214/aop/1008956692

Mathematical Reviews number (MathSciNet)
MR1849177

Zentralblatt MATH identifier
1015.60047

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

Keywords
Stochastic integral Malliavin calculus Ito's formula fractional Brownian motion

Citation

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


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