Related papers: Estimation of the Hurst parameter from discrete no…

We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter $H<1/2$ and the mean of its stationary…

We investigate here the Central Limit Theorem of the Increment Ratio Statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer-Major theorems and an…

We consider the simulation of sample paths of a fractional Brownian motion with small values of the Hurst index and estimate the behavior of the expected maximum. We prove that, for each fixed $N$, the error of approximation $\mathbf…

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in…

In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index…

Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…

The Hurst coefficient $H$ of a stochastic fractal signal is estimated using the function $\sigma_{MA}^2=\frac{1}{N_{max}-n}\sum_{i=n}^{N_{max}} [y(i)-\widetilde{y}_n(i)]^2$, where $\widetilde{y}_n(i)$ is defined as $1/n \sum_{k=0}^{n-1}…

The paper suggests a way of stochastic integration of random integrands with respect to fractional Brownian motion with the Hurst parameter H> 1/2. The integral is defined initially on the processes that are "piecewise" predictable on a…

In this article, we study the hyperbolic Anderson model in dimension 1, driven by a time-independent rough noise, i.e. the noise associated with the fractional Brownian motion of Hurst index $H \in (1/4,1/2)$. We prove that, with…

In the paper, we address parametric and non-parametric estimation for nonlinear stochastic differential equations with additive Hermite noise with possibly nonlinear scaling. We assume that a single trajectory of the solution is observed…

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\textgreater{}1/2$ and multiplicative noise component $\sigma$.…

Let $B_H(\cdot)$ be a fractional Brownian motion with Hurst parameter $H\in(0,1]$. Motivated by applications to maximal inequalities for fractional Brownian motion, in this note we derive bounds for…

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 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…

We study the Hardy-H\'enon parabolic equations on $\mathbb{R}^{N}$ ($N=2, 3$) under the effect of an additive fractional Brownian noise with Hurst parameter $H>\max\left(1/2, N/4\right).$ We show local existence and uniqueness of a mid…

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and…

Define the incremental fractional Brownian field $B_{H}(s+\tau)-B_{H}(s), H\in (0,1)$, where $B_{H}(s)$ is a standard fractional Brownian motion with Hurst index $H\in(0,1)$. In this paper we derive the exact asymptotic behaviour of the…

We propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and/or temporal scales. To this end, we extend the notion of a fractional Brownian bridge, defined as fractional…

We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…