出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：Let { BtH , t ≥ 0} be a fractional Brownian motion (fBm) with Hurst index H ∈ (1/2,1) and let {ξ n , n ≥ 0} be a sequence of centered random variables with stationary, long-range dependence increments. For every integer m ≥ 1 we define the random series Un ( m,H,f ), n ≥ 1 by Un ( m,H,f ) ≡ n-mH ∑ 0 ≤ j 1, j 2, …, jm < ∞ f ( j 1/ n , j 2/ n , …, jm/n )ξ j 1ξ j 2…ξ jm, where f : R + m → R is a deterministic function. Then the convergence Un ( m,H,f ) → d ∫ R + m f ( t 1, t 2,…, tm ) dB t 1 H dB t 2H … dB tmH ( n → ∞) is proved to hold for every integer m ≥ 1 under suitable conditions.
关键词：fractional Brownian motion;long-range dependence;multiple integral with respect to fractional Brownian motion
