V.V. Anh () (School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q. 4001, Australia Manuscript) C.N. Nguyen () (School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q. 4001, Australia Manuscript)
Abstract
Fractional Brownian motion (fBm) is fundamental in studying the phenomenon of long-range dependence in a wide range of fields. However, since fBm is not a semimartingale, some restrictions have been imposed on an fBm stochastic calculus. This paper studies fractional Riesz-Bessel motion (fRBm), which possesses many desirable properties of fBm and is a semimartingale for a range of its parameters. The prediction formula for fRBm is obtained, from which its semimartigale representation is established.
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