Related papers: Weak solutions of rough path SDE's via Girsanov

We study the linear transport equation \[ \frac{\partial}{\partial t} u ( t,x ) +b ( t,x ) \cdot \nabla u ( t,x ) + \nabla u ( t,x ) \cdot \frac{\partial}{\partial t} X ( t ) =0, \hspace{2em} u ( 0,x ) =u_{0} ( x ) \] where $b$ is a…

We study the existence of a unique solution to semilinear fractional backward doubly stochastic differential equation driven by a Brownian motion and a fractional Brownian motion with Hurst parameter less than 1/2. Here the stochastic…

Let $d\geq 2$. In this paper, we investigate the following stochastic differential equation (SDE) in ${\mathbb R}^d$ driven by Brownian motion $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqrt{2}{\rm d} W_t, $$ where $b$ belongs to the space ${\mathbb…

In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected…

We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution…

In this note, we take up the study of weak convergence for stochastic differential equations driven by a (Liouville) fractional Brownian motion $B$ with Hurst parameter $H\in(1/3,1/2)$. In the current paper, we approximate the…

In this paper, we study rough path properties of stochastic integrals of It\^{o}'s type and Stratonovich's type with respect to $G$-Brownian motion. The roughness of $G$-Brownian Motion is estimated and then the pathwise Norris lemma in…

We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…

This article is concerned with the existence of solution to the stochastic Degasperis-Procesi equation on $\mathbb{R}$ with an infinite dimensional multiplicative noise and integrable initial data. Writing the equation as a system composed…

We define a bona fide rough path solution for the Navier-Stokes equation with an additional rough transport term, and show that the SPDE on the three-dimensional torus driven by a fractional Brownian motion on $H^\sigma$ has solutions…

We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by cylindrical Brownian motion. The solutions are allowed to take values in general separable Banach…

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an…

In this paper, we obtain the existence and uniqueness theorem of $L^{p}$-solution for coupled forward-backward stochastic differential equations driven by G-Brownian motion (G-FBSDEs) with arbitrary $T$ under weakly coupling condition.…

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

We provide an existence and uniqueness result for mild solutions to rough partial differential equations in the framework of the semigroup approach. Applications to stochastic partial differential equations driven by infinite dimensional…

We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…

We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the lack of control of the reflection measure the proof uses some…

In this paper, we accomplish the existence and stability of the solution of a class of delay rough partial differential equations (DRPDEs). Moreover, we prove that the solution of DRPDEs can converge to that of RPDEs in sense of some…

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…

We consider a large class of nonlinear FPKEs with coefficients of Nemytskii-type depending explicitly on time and space, for which it is known that there exists a sufficiently Sobolev-regular distributional solution u in L^1 and L^\infty.…