Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156658 | Stochastic Processes and their Applications | 2012 | 46 Pages |
Abstract
For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in law with a correction term which is an Itô integral of fⴠwith respect to a Gaussian martingale independent of X. The proof uses Malliavin calculus and a central limit theorem from Nourdin and Nualart (2010) [8]. This formula was known for fBm with H=1/6 Nourdin et al. (2010) [9]. We extend this to a larger class of Gaussian processes.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Daniel Harnett, David Nualart,