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Integration questions related to fractional Brownian motion
Abstract. Let {BH(u)}u∈ℝ be a fractional Brownian motion (fBm) with index H∈(0, 1) and (BH) be the closure in L2(Ω) of the span Sp(BH) of the increments of fBm BH. It is well-known that, when BH =
Are classes of deterministic integrands for fractional Brownian motion on an interval complete
Let BH be a fractional Brownian motion with self-similarity parameter H e (0, 1) and a > 0 be a fixed real number. Consider the integral fa f(u)dBH(u), where f belongs to a class of non-random
Long-Range Dependence and Self-Similarity
This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to
Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed
Consider M independent and identically distributed renewal-reward processes with heavy-tailed renewals and rewards that have either finite variance or heavy tails. Let W*(Ty, M), y E [0, 1], denote
Multifractal Random Walks as Fractional Wiener Integrals
TLDR
The key properties of multifractal random walks are studied, such as finiteness of moments and scaling, with respect to the chosen values of the self-similarity and infinite divisibility parameters.
Integral representations and properties of operator fractional Brownian motions
Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar, and (iii) stationary increment processes. They are the natural multivariate generalizations of the
DEFINITIONS AND REPRESENTATIONS OF MULTIVARIATE LONG‐RANGE DEPENDENT TIME SERIES
The notion of multivariate long‐range dependence is reexamined here from the perspectives of time and spectral domains. The role of the so‐called phase parameters is clarified and stressed
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