Related papers: Non-degeneracy of Wiener functionals arising from …

Malliavin calculus provides a characterization of the centered model in regularity structures that is stable under removing the small-scale cut-off. In conjunction with a spectral gap inequality, it yields the stochastic estimates of the…

Following the approach and the terminology introduced in [A. Deya and R. Schott, On the rough paths approach to non-commutative stochastic calculus, J. Funct. Anal., 2013], we construct a product L{\'e}vy area above the $q$-Brownian motion…

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.…

The integration-by-parts formula discovered by Malliavin for the Ito map on Wiener space is proved using the two-parameter stochastic calculus. It is also shown that the solution of a one-parameter stochastic differential equation driven by…

For a class of piecewise deterministic Markov processes we introduce a stochastic calculus which is a certain non-Gaussian counterpart to the classical Malliavin calculus. As an application we investigate the regularity of densities of…

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…

Via a special transform and by using the techniques of the Malliavin calculus, we analyze the density of the solution to a stochastic differential equation with unbounded drift.

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…

We examine existence and uniqueness of strong solutions of multi-dimensional mean-field stochastic differential equations with irregular drift coefficients. Furthermore, we establish Malliavin differentiability of the solution and show…

We study counterfactual stochastic optimization of conditional loss functionals under misspecified and noisy gradient information. The difficulty is that when the conditioning event has vanishing or zero probability, naive Monte Carlo…

The theta process is a stochastic process of number theoretical origin arising as a scaling limit of quadratic Weyl sums. It can be described in terms of the geodesic flow and an automorphic function on a homogeneous space. This process has…

This paper introduces the path derivatives, in the spirit of Dupire's functional It\^o calculus, for the controlled paths in the rough path theory with possibly non-geometric rough paths. The theory allows us to deal with rough integration…

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic 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…

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.…

The stochastic partial differential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due to adsorption and desorption mechanisms involved in surface…

We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove the existence of densities for a class of singular SPDEs. Both of these results are…

We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate,…

We consider the class of non-linear stochastic partial differential equations studied in \cite{conusdalang}. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are…

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…