Related papers: Regularisation by fractional noise for one-dimensi…
In the present paper, we study the existence and blow-up behavior to the following stochastic non-local reaction-diffusion equation: \begin{equation*} \left\{ \begin{aligned} du(t,x)&=\left[(\Delta+\gamma) u(t,x)+\int_{D}u^{q}(t,y)dy…
The solution $X_n$ to a nonlinear stochastic differential equation of the form $dX_n(t)+A_n(t)X_n(t)\,dt-\tfrac12\sum_{j=1}^N(B_j^n(t))^2X_n(t)\,dt=\sum_{j=1}^N B_j^n(t)X_n(t)d\beta_j^n(t)+f_n(t)\,dt$, $X_n(0)=x$, where $\beta_j^n$ is a…
In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…
This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density…
We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the…
Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the fractional Bessel process. It\^{o}'s formula for…
In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness…
We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator estimates, we gain the existence and uniqueness of…
We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian…
In this paper we show that under some assumptions, for a $d$-dimensional fractional Brownian motion with Hurst parameter $H>1/2$, the density of solution of stochastic differential equation driven by it has a short-time expansion similar to…
The well-posedness is investigated for distribution dependent stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (\ff {\sq 5-1} 2,1)$ and distribution dependent multiplicative noise. To this…
In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…
In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the…
We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak…
This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a…
In this paper, we develop a Young integration theory in dimension 2 which will allow us to solve a non-linear one dimensional wave equation driven by an arbitrary signal whose rectangular increments satisfy some H\"{o}lder regularity…
We prove the existence of solutions for the stochastic differential equation $dX_t=b(t,X_{t-})dZ_t+a(t,X_t)dt, X_0\in\R, t\ge 0,$ with only measurable coefficients $a$ and $b$ satisfying the condition $0<\mu\le |b(t,x)|\le \nu$ and…
In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\rm d} X_t = b(t,X_t) {\rm d} t + {\rm d} B_{t},\ 0\leq t\leq T,\ X_0 = x \in \mathbb{R}^d,$$ where the drift coefficient $b:[0,T]\times…
This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…
In this paper we prove the existence of strong solutions to a SDE with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<1/2. Here the generalized drift is given as the local time of…