Related papers: Fractional Brownian Motion with Variable Hurst Par…
This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst…
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures $M[0,t], 0\le t\le1$. In this paper we obtain an extension of this process, referred to as multifractal…
We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst…
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate,…
We study the existence of a unique solution to semilinear fractional backward doubly stochastic differential equation driven by a Brownian motion and a fractional Brownian motion with Hurst parameter less than 1/2. Here the stochastic…
It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…
We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.
This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density…
Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal…
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…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter $\hat{\cal H} \in ( 1/2, 1)$. Using fixed point techniques, a…
In this presentation, we introduce a new method for change point analysis on the Hurst index for a piecewise fractional Brownian motion. We first set the model and the statistical problem. The proposed method is a transposition of the FDpV…
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale…
For fractional Brownian motion with Hurst parameter H the Berman constant is defined. In this paper we consider a general random field (rf) Z that is a spectral rf of some stationary max-stable rf X and derive the properties of the…
In this paper, we study the H\"older regularity of set-indexed stochastic processes defined in the framework of Ivanoff-Merzbach. The first key result is a Kolmogorov-like H\"older-continuity Theorem, whose novelty is illustrated on an…
We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are…