On limiting distributions of nonlinear functions of noisy Gaussian sequences
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 10 (4) , 417-430
- https://doi.org/10.1080/07362999208809280
Abstract
Let {Xn, n∊Z} be a mean-zero and variance-one stationary Gaussian process with long-range dependence. Given functions G(x) h(x,y) and H(x,y), and an i.i.d. sequence {Yn, n∊Z} which is independent of {Xn } we study the limiting distribution of , and compare it with the known results on the limiting distribution ofKeywords
This publication has 5 references indexed in Scilit:
- Central limit theorems for non-linear functionals of Gaussian fieldsJournal of Multivariate Analysis, 1983
- Convergence of integrated processes of arbitrary Hermite rankProbability Theory and Related Fields, 1979
- Non-central limit theorems for non-linear functional of Gaussian fieldsProbability Theory and Related Fields, 1979
- Probability TheoryPublished by Springer Nature ,1978
- Weak convergence to fractional brownian motion and to the rosenblatt processProbability Theory and Related Fields, 1975