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Stochastic Calculus with Respect to Gaussian Processes

Alos, Elisa
; 
Mazet, Olivier
; 
Nualart, David
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Abstract
In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt=∫t0K(t,s)dWs, 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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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1008956692.
Date
2001-12-05
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Institute of Mathematical Statistics
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Mathematics Scholarly Works
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Keywords
Stochastic integral, Malliavin calculus, Ito's formula, fractional Brownian motion
Citation
Alòs, Elisa ,1 2; and Mazet, Olivier; Nualart, David. Stochastic Calculus with Respect to Gaussian Processes. Ann. Probab. 29 (2001), no. 2, 766--801. http://dx.doi.org/10.1214/aop/1008956692.
URI
https://hdl.handle.net/1808/17052
DOI
10.1214/aop/1008956692
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