## Annals of Probability

### Stochastic Calculus with Respect to Gaussian Processes

#### 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

https://projecteuclid.org/euclid.aop/1008956692

Digital Object Identifier
doi:10.1214/aop/1008956692

Mathematical Reviews number (MathSciNet)
MR1849177

Zentralblatt MATH identifier
1015.60047

#### 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