Related papers: Malliavin differentiability of solutions of rough …

We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove…

We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…

We study a class of linear first and second order partial differential equations driven by weak geometric $p$-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving…

Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H \in (1/3, 1/2]$.

We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…

We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2.…

We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of…

We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's…

Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to…

In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a H\"older continuous function with parameter greater that 1/2 via the Young integration setting. Then some…

As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds…

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…

In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, whose solution admits a smooth density with respect to Lebesgue's measure. The result is…

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…

We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation…

We consider stochastic differential equations dY=V(Y)dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Y(t) admits a density for t in (0,T] provided (i) the vector fields…

Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance.…

Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results…

For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of its solution are established. It is also proved that the solution…

We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with…