On the characteristics of a class of Gaussian processes within the white noise space setting

2009/09/23 by Daniel Alpay, Alpay, Daniel, Haim Attia +3 · 1 citation
Mathematics · #47B32 #60G15 #60G22 #60H40 #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #math.CV #math.PR #msc:47B32 #msc:60G15 #msc:60G22 #msc:60H40

paper · pdf · doi:10.48550/arxiv.0909.4267

arxiv created 2009/09/23 · arxiv updated 2009/12/01

Abstract

Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form, studied by Schoenberg, von Neumann and Krein.

Cited by

• Superoscillations and the Klein-Gordon equation via the Fourier method

Related

• White noise based stochastic calculus associated with a class of Gaussian processes
• Stochastic Calculus with respect to Gaussian Processes: Part I
• A class of Gaussian processes with fractional spectral measures
• A class of infinite-dimensional Gaussian processes defined through generalized fractional operators
• The Properties of Fractional Gaussian Process and Their Applications