The Moduli of Continuity for Operator Fractional Brownian Motion

Wensheng Wang ()
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Wensheng Wang: Hangzhou Dianzi University

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2097-2120

Abstract: Abstract The almost-sure sample path behavior of the operator fractional Brownian motion with exponent D, including multivariate fractional Brownian motion, is investigated. In particular, the global and the local moduli of continuity of the sample paths are established. These results show that the global and the local moduli of continuity of the sample paths are completely determined by the real parts of the eigenvalues of the exponent D, as well as the covariance matrix at some unit vector. These results are applicable to multivariate fractional Brownian motion.

Keywords: Operator fractional Brownian motion; Operator-self-similarity; Multivariate fractional Brownian motion; Modulus of continuity; Law of the iterated logarithm; Strong local nondeterminism; 60G51; 60G17; 60E07; 60J30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01307-z

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