Convergence of weighted sums of random variables with long-range dependence
Tài liệu tham khảo
Avram, 1986, Weak convergence of moving averages with infinite variance., 399
Billingsley, 1968
Bingham, 1987
Davydov, 1970, The invariance principle for stationary processes, Theory Probab. Appl., 15, 487, 10.1137/1115050
Kasahara, 1986, Functional limit theorems for weighted sums of i.i.d. random variables, Probab. Theory Related Fields, 72, 161, 10.1007/BF00699101
Kasahara, 1988, Weighted sums of i.i.d. random variables attracted to integrals of stable processes, Probab. Theory Related Fields, 78, 75, 10.1007/BF00718037
Mandelbrot, 1982
Pipiras, V., Taqqu, M.S., 1998. Convergence of the Weierstrass–Mandelbrot process to fractional Brownian motion. Preprint.
Pipiras, V., Taqqu, M.S., 2000a. Integration questions related to fractional Brownian motion. Preprint 1999. Probability Theory and Related Fields, to appear.
Pipiras, 2000, The Weierstrass-Mandelbrot process provides a series approximation to the harmonizable fractional stable motion., 161
Samko, 1993
Samorodnitsky, 1994
Taqqu, 1975, Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrsch. Verwandte Gebiete, 31, 287, 10.1007/BF00532868
Zygmund, 1979