Convergence of Weighted Sums of Products of Random Variables with Long-Range Dependence

摘要: Let {BtH,t ≥ 0} be a fractional Brownian motion (fBm) with Hurst index H ∈ (1/2,1) and let {ξn,n sequence of centered random variables stationary, long-range dependence increments. For every integer m 1 we define the series Un(m,H,f), n by Un(m,H,f) ≡ n-mH ∑ 0 ≤ j1, j2, …, jm < ∞  f (j1/n, j2/n, jm/n)ξj1ξj2…ξjm, where f : R+m → R is deterministic function. Then convergence →d  ∫R+m  f (t1, t2,…, tm)dBt1H dBt2H … dBtmH     (n ∞) proved to hold for under suitable conditions.