A WAVELET-BASED ALMOST-SURE UNIFORM APPROXIMATION OF FRACTIONAL BROWNIAN MOTION WITH A PARALLEL ALGORITHM

作者：Hong Dawei^*; Man Shushuang; Birget Jean Camille; Lun Desmond S

来源：Journal of Applied Probability, 2014, 51(1): 1-18.

DOI：10.1239/jap/1395771410

• Fractional Brownian motion
• wavelet expansion of stochastic integral
• almost-sure uniform approximation

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (B-t((H)))(t is an element of[0,1]) of Hurst index H is an element of (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H is an element of (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

• 出版日期2014-3
• 单位rutgers