Stationary Brownian motion in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e861" altimg="si303.svg"><mml:mrow><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>-plane: Reduction to a Riemann–Hilbert problem via Fourier transforms

Fourier Transforms of Stationary Processes

We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in tha...

On Brownian Motion in a Fluid with a Plane Boundary

A tensor product approach to the abstract partial fourier transforms over semi-direct product groups

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

Fourier plane filtering, Riesz transforms, and Singularities in Optics

Nowadays harmonic analysis and wavelet-based decomposition approaches play an important role in image processing naming applications as image denoising, segmentation, or compression methods among others. In particular, analytic or monogenic wavelet approaches have found entrance in image processing delivering additional phase and orientation information or may be used for scale-based demodulati...

Affine stationary processes with applications to fractional Brownian motion

ABSTIUCT In our previous work, we introduced a new class of nonstationary stochastic processes whose spectral representation is associated with the wavelet transforms and established a mathematical framework for the analysis of such processes 111. We refer to these processes as uffine stptionary processes. These processes are indexed by the affine p u p , or ax+b group, which can be though of a...