Related papers: Differential equations driven by rough paths with …

We consider a stochastic Volterra integral equation with regular path-dependent coefficients and a Brownian motion as integrator in a multidimensional setting. Under an imposed absolute continuity condition, the unique solution is a…

In the article, the rough path theory is extended to cover paths from the exponential Besov-Orlicz space \[B^\alpha_{\Phi_\beta,q}\quad\mbox{ for }\quad \alpha\in (1/3,1/2],\,\quad \Phi_\beta(x) \sim…

In this paper, we are devoted to the numerical methods for mean-field stochastic differential equations with jumps (MSDEJs). First by using the mean-field It\^o formula [Sun, Yang and Zhao, Numer. Math. Theor. Meth. Appl., 10 (2017),…

We consider a differential equation driven by a Brownian motion as well as a rough path. We prove a Girsanov-type result for this equation to construct a weak solution in the probabilistic sense.

We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…

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 introduce in this work a concept of rough driver that somehow provides a rough path-like analogue of an enriched object associated with time-dependent vector fields. We use the machinery of approximate flows to build the integration…

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…

We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…

We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It\^o's formula. Moreover, we study the solvability of the scalar valued stochastic differential…

Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional…

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 discuss regular and weak solutions to rough partial differential equations (RPDEs), thereby providing a (rough path-)wise view on important classes of SPDEs. In contrast to many previous works on RPDEs, our definition gives honest…

Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on…

In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions.…

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 contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…

Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…