Related papers: Rough Hurst function estimation
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with…
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and…
For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical…
We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
In this paper, we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$. We interpret these equations either in the sense of Young ($H>1/2$) or Stratonovich ($H=1/2$).…
We pursue our investigations, initiated in [8], about stochastic integration with respect to the non-commutative fractional Brownian motion (NC-fBm). Our main objective in this paper is to compare the pathwise constructions of [8] with a…
In this contribution, we extend the methodology proposed in Abry and Didier (2017) to obtain the first joint estimator of the real parts of the Hurst eigenvalues of $n$-variate OFBM. The procedure consists of a wavelet regression on the…
Fourier normal ordering \cite{Unt09bis} is a new algorithm to construct explicit rough paths over arbitrary H\"older-continuous multidimensional paths. We apply in this article the Fourier normal ordering ordering algorithm to the…
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…
We study the relationship between mixed stochastic differential equations and the corresponding rough path equations driven by standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. We establish a correction…
In this work we study fractal properties of rough differential equations driven by a fractional Brownian motions with Hurst parameter $H>\frac{1}{4}$. In particular, we show that the Hausdorff dimension of the sample paths of the solution…
A well-known class of non-stationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. In this paper, we study the homology groups of high-dimensional point cloud…
In this paper, we consider the problem of estimating the lead-lag parameter between two stochastic processes driven by fractional Brownian motions (fBMs) of the Hurst parameter greater than 1/2. First we propose a lead-lag model between two…
We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast…
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…
The Davenport spectrum is a modification of the classical Kolmogorov spectrum for the inertial range of turbulence that accounts for non-scaling low frequency behavior. Like the classical fractional Brownian motion vis-\`a-vis the…
In this note we consider stochastic differential equations driven by fractional Brownian motions (fBm) with Hurst parameter $H>1/3$. We prove that the corresponding modified Euler scheme and its Malliavin derivatives are integrable,…
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the…