ﻻ يوجد ملخص باللغة العربية
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non--Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares si
The rate at which dependencies between future and past observations decay in a random process may be quantified in terms of mixing coefficients. The latter in turn appear in strong laws of large numbers and concentration of measure results for depend
It is of fundamental importance to determine if and how hierarchical clustering is involved in large-scale structure formation of the universe. Hierarchical evolution is characterized by rules which specify how dark matter halos are formed by the mer
A new class of explicit Milstein schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these explici
We study the asymptotic behavior of solution of semi-linear PDEs. Neither periodicity nor ergodicity will be assumed. In return, we assume that the coefficients admit a limit in `{C}esaro sense. In such a case, the averaged coefficients could be disc