Stochastic Calculus with Respect to Gaussian Processes
Alòs, Elisa ,1 2 and ; Mazet, Olivier ; Nualart, David
Ann. Probab., Tome 29 (2001) no. 1, p. 766-801 / Harvested from Project Euclid
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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.
Publié le : 2001-04-14
Classification:  Stochastic integral,  Malliavin calculus,  Ito's formula,  fractional Brownian motion,  60N05,  60H07 
@article{1008956692,
     author = {Al\`os, Elisa ,1 2 and and Mazet, Olivier and Nualart, David},
     title = {Stochastic Calculus with Respect to Gaussian Processes},
     journal = {Ann. Probab.},
     volume = {29},
     number = {1},
     year = {2001},
     pages = { 766-801},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1008956692}
}

Alòs, Elisa ,1 2 and; Mazet, Olivier; Nualart, David. Stochastic Calculus with Respect to Gaussian Processes. Ann. Probab., Tome 29 (2001) no. 1, pp.  766-801. http://gdmltest.u-ga.fr/item/1008956692/