A self-similar Gaussian process

Abstract

Abstract. In this paper we introduce and study a self-similar Gaussian process denoted by S H , K ${{S^{H,\,K}}}$ with parameters H ∈ ( 0 , 1 ) ${{H\in (0,1)}}$ and K ∈ [ 0 , 1 ] ${{K\in [0,1]}}$ . This process generalizes the well-known fractional Brownian motion introduced by Mandelbrot and Van Ness [SIAM Rev. 10 (1968), no. 4, 422–437], the sub-fractional Brownian motion introduced by Bojdecki, Gorostiza and Talarczyket [Statist. Probab. Lett. 69 (2004), 405–419] and the Gaussian process introduced by Lei and Nualart [Statist. Probab. Lett. 79 (2009), 619–624] in order to obtain a decomposition in law of the bifractional Brownian motion.