## Abstract Fractal Brownian motion, also called fractional Brownian motion (fBm), is a class of stochastic processes characterized by a single parameter called the Hurst parameter, which is a real number between zero and one. fBm becomes ordinary standard Brownian motion when the parameter has the
Fractional Brownian motion via fractional Laplacian
β Scribed by Tomasz Bojdecki; Luis G. Gorostiza
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 61 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
A new and short proof of existence of the fractional Brownian ΓΏeld with exponent =2; β (0; 2], is given in terms of the fractional power of the Laplacian.
π SIMILAR VOLUMES
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.
Standard and fractional Brownian motions are known to be unsatisfactory models of asset prices. A new class of continuous-time stochastic processes, RFBM, is proposed to remedy some of the shortcomings of current models. RFBM lead to valuation formulas similar to Black}Scholes, but with volatility i
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