Related papers: Differential equations driven by rough paths: an a…

In this article we propose a new explicit Euler-type approximation method for stochastic differential equations (SDEs). In this method, Brownian increments in the recursion of the Euler method are replaced by suitable bounded functions of…

We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…

Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct…

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.

Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217,…

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…

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…

We give meaning to differential equations with a rough path term and a Brownian noise term as driving signals. Such differential equations as well as the question of regularity of the solution map arise naturally and we discuss two…

We propose a theory of linear differential equations driven by unbounded operator-valued rough signals. As an application we consider rough linear transport equations and more general linear hyperbolic symmetric systems of equations driven…

The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…

We construct the "expected signature matching" estimator for differential equations driven by rough paths and we prove its consistency and asymptotic normality. We use it to estimate parameters of a diffusion and a fractional diffusions,…

We prove existence and uniqueness results for (mild) solutions to some non-linear parabolic evolution equations with a rough forcing term. Our method of proof relies on a careful exploitation of the interplay between the spatial and time…

In [1], we proved the existence of solutions to reflected rough differential equations based on an idea of Euler approximation of the solutions which is due to Davie [6]. In this paper, we prove the existence theorem under weaker…

We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…

The dynamics of rough differential equations (RDEs) has recently received a lot of interest. For example, the existence of local random center manifolds for RDEs has been established. In this work, we present an approximation for local…

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…

A geometric p-rough path can be seen to be a genuine path of finite p-variation with values in a Lie group equipped with a natural distance. The group and its distance lift (R^{d},+,0) and its Euclidean distance. This approach allows us to…

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…