Stochastic Calculus with Respect to Gaussian Processes
Elisa ,1 2 and Alòs, Olivier Mazet and David Nualart
Source: Ann. Probab. Volume 29, Number 2 (2001), 766-801.
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.
Primary Subjects: 60N05, 60H07
Keywords: Stochastic integral; Malliavin calculus; Ito's formula; fractional Brownian motion
Full-text: Access granted (open access)
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1008956692
Digital Object Identifier: doi:10.1214/aop/1008956692
Mathematical Reviews number (MathSciNet):
MR1849177
Zentralblatt MATH identifier:
1015.60047
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