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Journal article
ON OPERATOR FRACTIONAL LEVY MOTION: INTEGRAL REPRESENTATIONS AND TIME-REVERSIBILITY
Advances in applied probability, v 54(2), pp 493-535
01 Jun 2022
Abstract
In this paper, we construct operator fractional Levy motion (ofLm), a broad class of infinitely divisible stochastic processes that are covariance operator self-similar and have wide-sense stationary increments. The ofLm class generalizes the univariate fractional Levy motion as well as the multivariate operator fractional Brownian motion (ofBm). OfLm can be divided into two types, namely, moving average (maofLm) and real harmonizable (rhofLm), both of which share the covariance structure of ofBm under assumptions. We show that maofLm and rhofLm admit stochastic integral representations in the time and Fourier domains, and establish their distinct small-and large-scale limiting behavior. We also characterize time-reversibility for ofLm through parametric conditions related to its Levy measure. In particular, we show that, under non-Gaussianity, the parametric conditions for time-reversibility are generally more restrictive than those for the Gaussian case (ofBm).
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Details
- Title
- ON OPERATOR FRACTIONAL LEVY MOTION: INTEGRAL REPRESENTATIONS AND TIME-REVERSIBILITY
- Creators
- B. Cooper Boniece - University of UtahGustavo Didier - Tulane University
- Publication Details
- Advances in applied probability, v 54(2), pp 493-535
- Publisher
- Cambridge Univ Press
- Number of pages
- 43
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000812842300006
- Scopus ID
- 2-s2.0-85132007956
- Other Identifier
- 991021861875404721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Statistics & Probability