In this paper some results for a stochastic calculus for a fractional Brownian motion are described. Some applications of this calculus are given. Some results of a spectral approach to fractional Gaussian noise, the formal derivative of fractional Brownian motion, are given.
On the large increments of fractional Brownian motion
โ Scribed by Charles El-Nouty
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 354 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0167-7152
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โฆ Synopsis
Let {BH(t), t ~>0} be a fractional Brownian motion with index 00. We establish some laws of the iterated logarithm for Vr.
๐ SIMILAR VOLUMES
Let X(t) (t ~ ~N) be a fractional Brownian motion of index ~ in R d.
We prove some maximal inequalities for fractional Brownian motions. These extend the Burkholder-Davis-Gundy inequalities for fractional Brownian motions. The methods are based on the integral representations of fractional Brownian motions with respect to a certain Gaussian martingale in terms of bet
approximation is good only if the frequency ( f ) is relatively large [14, pp. 155-158, 247]. Consequently, inaccuracy in We present new algorithms for simulation of fractional Brownian motion (fBm) which comprises a set of important random functions simulation of fBm, resulting from the Fourier fi