Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m--[infinity]. We also consider two examples....

It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval...

We show that a fractional Brownian motion with H'E(0,1) can be represented as an explicit transformation of a fractional Brownian motion with index H E(0,1). In particular, when H'=1/2, we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion. We work...

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 current research. These topics concern, but are not limited to, physical models that give rise to...

Let 0<[alpha][less-than-or-equals, slant]2 and let . Let {X(t),t[set membership, variant]T} be a linear fractional [alpha]-stable (0<[alpha][less-than-or-equals, slant]2) motion with scaling index H (0<H<1) and with symmetric [alpha]-stable random measure. Suppose that [psi] is a bounded real function with compact support [a,b] and at least one null moment. Let the sequence of the discrete wavelet coefficients of the process X beWe use a stochastic integral representation of the process X to describe the wavelet coefficients as [alpha]-stable integrals when H-1/[alpha]>-1. This stochastic representation is used to prove that the stochastic process of wavelet coefficients , with fixed scale index , is strictly stationary. Furthermore, a property of self-similarity of the wavelet coefficients of X is proved. This property has been the motivation of several...</[alpha][less-than-or-equals,>

Community shared bicycle systems, such as the Vélo'v program launched in Lyon in May 2005, are public transportation programs that can be studied as a complex system composed of interconnected stations that exchange bicycles. They generate digital footprints that reveal the activity in the city...

type="main" xml:id="jtsa12086-abs-0001"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 throughout. In particular, examples of causal (one-sided)...