Related papers: Euler scheme for stochastic functional differentia…
In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H…
We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way, following the approach of Gubinelli, we…
For degenerate stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H>1/2$, the derivative formulas are established by using Malliavin calculus and coupling method, respectively. Furthermore, we find…
The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\gamma$-H\"older continuous process with $\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than…
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in…
In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise,…
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution…
In this paper we present a new method for the construction of strong solutions of SDE's with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter H < 1/2. Furthermore, we prove…
The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter…
We develop an operator-theoretic formulation of stochastic calculus for fractional Brownian motion with Hurst parameter H in (0, 1/2). The approach is based on adjointness between stochastic integration and differentiation in the…
We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…
In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, with respect to fractional Brownian motion with Hurst parameter $H \in (1/2,1)$, for a large class of convex functions $f$ is considered. In…
This paper studies the existence and uniqueness of solution of It\^o type stochastic differential equation $dx(t)=b(t, x(t), \om)dt+\si(t,x(t), \om) d B(t)$, where $B(t)$ is a fractional Brownian motion of Hurst parameter $H>1/2$ and…
This paper develops an It\^o-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons' rough path framework. This approach is designed to fill…
In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show that there is a unique solution, which has…
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…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…