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Conditional Full Support of Gaussian Processes with Stationary Increments

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Dario Gasbarra ,
Tommi Sottinen  and
Harry van Zanten
Dario Gasbarra*
Affiliation:
University of Helsinki
Tommi Sottinen*
Affiliation:
University of Vaasa
Harry van Zanten*
Affiliation:
Eindhoven University of Technology
*
∗Current address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FIN-40014, Jyväskylä, Finland. Email address: dario.d.gasbarra@jyu.fi
∗∗Postal address: Department of Mathematics and Statistics, University of Vaasa, PO Box 700, FIN-65101, Vaasa, Finland. Email address: tommi.sottinen@uwasa.fi
∗∗∗Postal address: Department of Mathematics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: j.h.v.zanten@tue.nl
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Abstract

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We investigate the conditional full support (CFS) property, introduced in Guasoni et al. (2008a), for Gaussian processes with stationary increments. We give integrability conditions on the spectral measure of such a process which ensure that the process has CFS or not. In particular, the general results imply that, for a process with spectral density f such that f(λ) ∼ c1λpe−c2λq for λ → ∞ (with necessarily p < 1 if q = 0), the CFS property holds if and only if q < 1.

Keywords

Conditional full supportconditional lawGaussian processprocesses with stationary incrementsspectral measure

MSC classification

Secondary: 60G15: Gaussian processes 60G30: Continuity and singularity of induced measures
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 561 - 568
Copyright
Copyright © Applied Probability Trust 2011 

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