Journal articles
Year
2023
Abstract
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their
covariance function. In particular, we propose a new simple rate-optimal
series expansion for fractional Brownian motion. The convergence of the
latter series holds in mean square and uniformly almost surely, with a rateoptimal decay of the remainder of the series. We also develop a general
framework of convergent series expansions for certain classes of Gaussian
processes with stationarity. Finally, an application to optimal functional
quantization is described.
NDAOUD, M. (2023). Harmonic analysis meets stationarity: A general framework for series expansions of special Gaussian processes. Bernoulli: A Journal of Mathematical Statistics and Probability, 29(3), pp. 2295 – 2317.