Related papers: Wavelet eigenvalue regression for $n$-variate oper…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of…
The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…
We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…
The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in {\mathbb{R}_{+}\times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older…
We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…
In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet…
This paper is devoted to the study of the eigenvalues of the Wishart process which are the analogof the Dyson Brownian Motion for covariance matrices. Such processes were in particular studied byBru. The mean field convergence of the…
We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of…
In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of $L^q$ norms of the (possibly non-selfadjoint) potential. They proved that for $1<q<4/3$ all…
We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion $B_t$ of known Hurst index $H$, based on weighted functionals of the single time square displacement. We show that for a certain choice…
The $d$-dimensional fractional Brownian motion (FBM for short) $B_t=((B_t^{(1)},...,B_t^{(d)}),t\in\mathbb{R})$ with Hurst exponent $\alpha$, $\alpha\in(0,1)$, is a $d$-dimensional centered, self-similar Gaussian process with covariance…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
The so-called Hadamard fractional Brownian motion, as defined in Beghin et al. (2025) by means of Hadamard fractional operators, is a Gaussian process which shares some properties with standard Brownian motion (such as the one-dimensional…
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller…
We introduce the stochastic process of incremental multifractional Brownian motion (IMFBM), which locally behaves like fractional Brownian motion with a given local Hurst exponent and diffusivity. When these parameters change as function of…