Multidimensional Lévy White Noise in Weighted Besov Spaces
J. Fageot, A. Fallah, M. Unser
Stochastic Processes and Their Applications, vol. 127, no. 5, pp. 1599–1621, May 2017.
In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrability properties of the noise using the indices introduced by Blumenthal, Getoor, and Pruitt. Our techniques rely on wavelet methods and generalized moments estimates for Lévy noises.
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AUTHOR="Fageot, J. and Fallah, A. and Unser, M.",
TITLE="Multidimensional {L}{\'{e}}vy White Noise in Weighted {B}esov
Spaces",
JOURNAL="Stochastic Processes and Their Applications",
YEAR="2017",
volume="127",
number="5",
pages="1599--1621",
month="May",
note="")
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