Mathematics – Statistics Theory
Scientific paper
2010-10-08
Bernoulli 2010, Vol. 16, No. 2, 389-417
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.3150/09-BEJ223 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/09-BEJ223
We approximate the solution of some linear systems of SDEs driven by a fractional Brownian motion $B^H$ with Hurst parameter $H\in(\frac{1}{2},1)$ in the Wick--It\^{o} sense, including a geometric fractional Brownian motion. To this end, we apply a Donsker-type approximation of the fractional Brownian motion by disturbed binary random walks due to Sottinen. Moreover, we replace the rather complicated Wick products by their discrete counterpart, acting on the binary variables, in the corresponding systems of Wick difference equations. As the solutions of the SDEs admit series representations in terms of Wick powers, a key to the proof of our Euler scheme is an approximation of the Hermite recursion formula for the Wick powers of $B^H$.
Bender Christian
Parczewski Peter
No associations
LandOfFree
Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-486400