Related papers: Fractional Cox--Ingersoll--Ross process with non-z…

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…

Let X^{1}, X^{2} be two independent (two-sided) fractional Brownian motions having the same Hurst parameter H in (0,1), and let Y be a standard (one-sided) Brownian motion independent of (X^{1},X^{2}). In dimension 2, fractional Brownian…

Let $X_H(t), t\ge 0$ be a fractional Brownian motion with Hurst index $H\in(0,1}$ and define a gamma-reflected process $W_\Ga(t)=X_H(t)-ct-\gammainf_{s\in[0,t]}\left(X_H(s)-cs \right)$, $t\ge0$ with $c>0,\gamma \in [0,1]$ two given…

We will consider the following stochastic differential equation (SDE): \begin{equation} X_t=X_0+\int_0^tb(X_s,\theta_0)ds+\sigma B_t,~~~t\in(0,T], \end{equation} where $\{B_t\}_{t\ge 0}$ is a fractional Brownian motion with Hurst index…

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…

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 $\sigma$.…

In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…

Consider $Z^f_t(u)=\int_0^{tu}f(N_s) ds$, $t>0$, $u\in[0,1]$, where $N=(N_t)_{t\in\mathbb{R}}$ is a normal process and $f$ is a measurable real-valued function satisfying $Ef(N_0)^2<\infty$ and $Ef(N_0)=0$. If the dependence is sufficiently…

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…

We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form $\int _0^ts^{\gamma}dW_s$, where $W$ is a Wiener process, $\gamma >0$.

Let $(X_1, \xi_1), (X_2,\xi_2),\ldots$ be i.i.d.~copies of a pair $(X,\xi)$ where $X$ is a random process with paths in the Skorokhod space $D[0,\infty)$ and $\xi$ is a positive random variable. Define $S_k := \xi_1+\ldots+\xi_k$, $k \in…

This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…

We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…

In this paper, we consider a one-dimensional Cox-Ingersoll-Ross (CIR) process whose drift coefficient depends on unknown parameters. Considering the process discretely observed at high frequency, we prove the local asymptotic normality…

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…

In this work, we present a detailed analysis on the exact expression of the $L^2$-norm of the symmetric-Stratonovich stochastic integral driven by a multi-dimensional fractional Brownian motion $B$ with parameter $\frac{1}{4} < H <…

We consider equidistant approximations of stochastic integrals driven by H\"older continuous Gaussian processes of order $H>\frac12$ with discontinuous integrands involving bounded variation functions. We give exact rate of convergence in…

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…