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Integration questions related to fractional Brownian motion

- V. Pipiras, M. Taqqu
- Mathematics
- 2000

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 =… Expand

Are classes of deterministic integrands for fractional Brownian motion on an interval complete

- V. Pipiras, M. Taqqu
- Mathematics
- 2001

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… Expand

Long-Range Dependence and Self-Similarity

- V. Pipiras, M. Taqqu
- Mathematics
- 18 April 2017

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… Expand

Estimation of the self-similarity parameter in linear fractional stable motion

- Stilian A. Stoev, V. Pipiras, M. Taqqu
- MathematicsSignal Process.
- 1 December 2002

Regularization and integral representations of Hermite processes

- V. Pipiras, M. Taqqu
- Mathematics
- 1 December 2010

Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed

- V. Pipiras, M. Taqqu, J. Levy
- Mathematics
- 1 February 2004

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… Expand

Convergence of weighted sums of random variables with long-range dependence (

- V. Pipiras, M. Taqqu
- Mathematics
- 1 November 2000

Multifractal Random Walks as Fractional Wiener Integrals

- P. Abry, P. Chainais, L. Coutin, V. Pipiras
- MathematicsIEEE Transactions on Information Theory
- 1 August 2009

TLDR

Integral representations and properties of operator fractional Brownian motions

- G. Didier, V. Pipiras
- Mathematics
- 1 February 2011

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… Expand

DEFINITIONS AND REPRESENTATIONS OF MULTIVARIATE LONG‐RANGE DEPENDENT TIME SERIES

- Stefanos Kechagias, V. Pipiras
- Mathematics
- 1 January 2015

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… Expand

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