Related papers: On mixed fractional SDEs with discontinuous drift …
We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence…
We obtain a stochastic differential equation (SDE) satisfied by the first $n$ coordinates of a Brownian motion on the unit sphere in $\mathbb{R}^{n+\ell}$. The SDE has non-Lipschitz coefficients but we are able to provide an analysis of…
We study quasi-linear stochastic partial differential equations with discontinuous drift coefficients. Existence and uniqueness of a solution is already known under weaker conditions on the drift, but we are interested in the regularity of…
This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying…
This paper studies the weak and strong solutions to the stochastic differential equation $ dX(t)=-\frac12 \dot W(X(t))dt+d\mathcal{B}(t)$, where $(\mathcal{B}(t), t\ge 0)$ is a standard Brownian motion and $W(x)$ is a two sided Brownian…
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…
We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entire flow of its time marginals. We establish the existence and…
We derive the strong consistency of the least squares estimator for the drift coefficient of a fractional stochastic differential system. The drift coeffcient is one-sided dissipative Lipschitz and the driving noise is additive and…
Let us consider a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)|x|^\alpha/t^\beta$. This process can be viewed as a distorted Brownian…
In this paper, we study a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H>\ff 1 2$. The drift term of the equation is locally Lipschitz and unbounded in the…
The aim of the book is to present some recent results in the theory of stochastic It\^o equations with singular deterministic part (drift) and its applications to second-order elliptic and parabolic equations with singular first-order…
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…
In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation $dX(t)={\rm div} [\frac{\nabla X(t)}{|\nabla X(t)|}]dt+X(t)dW(t) in…
In this paper, we study averaging principle for a class of McKean-Vlasov stochastic differential equations (SDEs) that contain multiplicative fractional noise with Hurst parameter $H > $ 1/2 and highly oscillatory drift coefficient. Here…
In this work we present a condition for the regularity, in both space and Malliavin sense, of strong solutions to SDEs driven by Brownian motion. We conjecture that this condition is optimal. As a consequence, we are able to improve the…
The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional It\^o diffusion that almost surely converges to a weak solution of the given stochastic differential equation. Under suitable conditions, the…
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an $m$-dimensional Brownian motion and a $d$-dimensional canonical process with uniform Lipschitzian coefficients. Such…
Let $X$ be the sum of a fractional Brownian motion with Hurst parameter $H$ and an absolutely continuous and adapted drift process. We establish a simple criterion that guarantees that the law of $X$ is absolutely continuous with respect to…
We introduce a fractional stochastic heat equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize…