Related papers: First Order Linear Marcus SPDEs

We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…

We derive a Tanaka-type formula for the solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (fBm) with Hurst parameter $H > \frac{1}{2}$. While Tanaka formulas for the fractional Brownian motion itself…

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola…

We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution…

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in…

We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1/2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on…

Let X be the solution of the multidimensional stochastic differential equationdX(t) = b(t, X(t)) dt + sigma(t, X(t)) dW(t)\, with X(0)=x where W is a standard Brownian motion. We show that when b is measurable and sigma is in an appropriate…

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to…

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.

In this article, well-posedness of stochastic anisotropic $p$-Laplace equation driven by L\'evy noise is shown. Such an equation in deterministic setting was considered by Lions [7]. The results obtained in this article can be applied to…

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional brownian motion and the multifractional…

We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The…

In this paper we study the stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs for short). We extend the notion of conditional $G$-expectation from deterministic time to the more general optional time situation. Then,…

In this paper we study the pathwise uniqueness of solution to the following stochastic partial differential equation (SPDE) with H\"older continuous coefficient: \begin{eqnarray*} \frac{\partial X_t(x)}{\partial t}=\frac{1}{2} \Delta X_t(x)…

We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…

We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. We show that for any suitable initial data there exists a pathwise unique, global solution to…