Related papers: Elliptic stochastic partial differential equations…
In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of…
This work is concerned with existence and uniqueness of solutions to the reflection problem for linear parabolic equation with multiplicative Gaussian noise.
In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a…
We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and -1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a…
In this paper we study reflected backward stochastic differential equations with a continuous, linear growth coefficient and two barriers which belong to L^2. We prove that there exists at least by penalization method.
In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz…
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence…
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…
In this article, we established a large deviation principle for invariant measures of solutions of stochastic partial differential equations with two reflecting walls driven by space-time white noise.
In this paper, we focus on the existence of the density for the law of the solutions to parabolic stochastic partial differential equations with two reflecting walls. The main tool is Malliavin calculus.
We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove…
We study lattice approximations of reflected stochastic elliptic equations driven by white noise on a bounded domain in $\mathbb{R}^d,\ d=1,2,3$. The convergence of the scheme is established.
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space--time white noise and contains a double…
This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.
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…
In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson…
We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the…
In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include…
Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the…