arXiv subjects
Publications and source records attributed to Olga Polosmak.
The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed technique are shown for several classes of stochastic processes. In particular, the main theorem is adjusted to the fractional Brownian motion case. New results on the rate of convergence of the wavelet expansions in the space $C([0,T])$ are also presented.
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
The article presents new results on convergence in $L_p([0,T])$ of wavelet expansions of $φ$-sub-Gaussian random processes. The convergence rate of the expansions is obtained. Specifications of the obtained results are discussed.