Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the long range dependence of time-changed mixed fractional Brownian motion model
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A time-changed mixed fractional Brownian motion is an iterated process constructed as the superposition of mixed fractional Brownian motion and other process. In this paper we consider mixed fractional Brownian motion of parameters a, b and Hin(0, 1) time-changed by two processes, gamma and tempered stable subordinators. We present their main properties paying main attention to the long range dependence. We deduce that the fractional Brownian motion time-changed by gamma and tempered stable subordinators has long range dependence property for all Hin(0, 1).
rate research
Read More
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well known mixed fractional Brownian motion introduced by Cheridito [10] and the generalized fractional Brownian motion introduced by Zili [31]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long range dependence properties of this process.
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime.
Let $G$ be a non--linear function of a Gaussian process ${X_t}_{tinmathbb{Z}}$ with long--range dependence. The resulting process ${G(X_t)}_{tinmathbb{Z}}$ is not Gaussian when $G$ is not linear. We consider random wavelet coefficients associated with ${G(X_t)}_{tinmathbb{Z}}$ and the corresponding wavelet scalogram which is the average of squares of wavelet coefficients over locations. We obtain the asymptotic behavior of the scalogram as the number of observations and scales tend to infinity. It is known that when $G$ is a Hermite polynomial of any order, then the limit is either the Gaussian or the Rosenblatt distribution, that is, the limit can be represented by a multiple Wiener-It^o integral of order one or two. We show, however, that there are large classes of functions $G$ which yield a higher order Hermite distribution, that is, the limit can be represented by a a multiple Wiener-It^o integral of order greater than two.
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the second order. This in turn allows to compute the exact $L_2$-small ball probabilities, previously known only at logarithmic precision. The obtained expressions show an interesting stratification of scales, which occurs at certain values of the Hurst parameter of the fractional component. Some of them have been previously encountered in other problems involving such mixtures.
Let $D$ be an unbounded domain in $RR^d$ with $dgeq 3$. We show that if $D$ contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on $overline D$ is transient. Next assume that RBM $X$ on $overline D$ is transient and let $Y$ be its time change by Revuz measure ${bf 1}_D(x) m(x)dx$ for a strictly positive continuous integrable function $m$ on $overline D$. We further show that if there is some $r>0$ so that $Dsetminus overline {B(0, r)}$ is an unbounded uniform domain, then $Y$ admits one and only one symmetric diffusion that genuinely extends it and admits no killings. In other words, in this case $X$ (or equivalently, $Y$) has a unique Martin boundary point at infinity.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
