Limits of bifractional Brownian noises

2008/10/27 by Makoto Maejima, Maejima, Makoto, Ciprian Tudor +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.0810.4764

arxiv created 2008/10/27 · arxiv updated 2009/12/01

Abstract

Let B^H,K=(B^H,K_t, t≥ 0) be a bifractional Brownian motion with two parameters H∈ (0,1) and K∈(0,1]. The main result of this paper is that the increment process generated by the bifractional Brownian motion (B^H,K_h+t -B^H,K_h, t≥ 0) converges when h→ ∞ to (2^(1-K)/2B^HK_t, t≥ 0), where (B^HK_t, t≥ 0) is the fractional Brownian motion with Hurst index HK. We also study the behavior of the noise associated to the bifractional Brownian motion and limit theorems to B^H,K.

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