We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

This paper studies first a result of existence and uniqueness of the solution to a backward stochastic differential equation driven by an infinite dimensional martingale. Then, we apply this result to find a unique solution to a backward stochastic partial differential equation in infinite dimensions. The filtration considered is an arbitrary rightcontinuous filtration, not necessarily the natu...

In this paper we study well-posedness of a second order SPDE with multiplicative noise on the torus T = [0, 2π]. The equation is considered in L((0, T )×Ω;L(T)) for p, q ∈ (1,∞). It is well-known that if the noise is of gradient type, one needs a stochastic parabolicity condition on the coefficients for well-posedness with p = q = 2. In this paper we investigate whether the well-posedness depen...

We review the manifold projection method for stochastic nonlinear filtering in a more general setting than in our previous paper in Geometric Science of Information 2013. We still use a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic partial differential equation for the optimal filter onto a finite dimensional exponential or mixture fa...

We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

‎in this paper‎, ‎we present a novel approach for image selective smoothing by the evolution of two paired nonlinear‎ ‎partial differential equations‎. ‎the distribution coefficient in de-noising equation controls the speed of distribution‎, ‎and is‎ ‎determined by the edge-strength function‎. ‎in the previous works‎, ‎the edge-strength function depends on isotropic‎ ‎smoothing of the image‎...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...

although there are many methods for image denoising, but partial differential equation (pde) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (mri). the main advantage of pde-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...