Limits of bifractional Brownian noises

Abstract

Let B H,K = B H,K ,t ‚ 0 be a bifractional Brownian motion with two parameters H 2 (0,1) and K 2 (0,1). The main result of this paper is that the increment process generated by the bifractional Brownian motion B H,K+t i B H,K h ,t ‚ 0 converges when h ! 1 to 2 (1iK)/2 B HK t ,t ‚ 0 , where B HK ,t ‚ 0 is the fractional Brownian motion with Hurst index HK. We also study the behavior of the noise associated to the bifractional Brow- nian motion and limit theorems to B H,K.