Journal article
A class of Gaussian processes with fractional spectral measures
Journal of functional analysis, Vol.261(2), pp.507-541
2011
DOI: 10.1016/j.jfa.2011.03.012
Abstract
We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from σ when σ is in one of the classes of affine selfsimilar measures. Our analysis makes use of Kondratiev white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).
Details
- Title: Subtitle
- A class of Gaussian processes with fractional spectral measures
- Creators
- Daniel Alpay - Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Beʼer Sheva 84105, IsraelPalle Jorgensen - Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, IA 52242-1419, USADavid Levanony - Department of Electrical Engineering, Ben Gurion University of the Negev, P.O.B. 653, Beʼer Sheva 84105, Israel
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.261(2), pp.507-541
- DOI
- 10.1016/j.jfa.2011.03.012
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Grant note
- Department of Mathematics, Ben Gurion University of the Negev 1023/07 / Israel Science Foundation
- Language
- English
- Date published
- 2011
- Academic Unit
- Mathematics
- Record Identifier
- 9983985814602771
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