Gauss噪声扰动下的FitzHugh-Nagumo系统的随机稳定性

在Gauss噪声扰动下FitzHugh-Nagumo系统的随机稳定性是该文的研究目的．通过研究随机FitzHugh-Nagumo系统的动力学行为, 证明其存在唯一的、具有指数混合速度的不变测度．最后, 考察当噪声趋于0时不变测度的渐近行为．     

A class of Gaussian processes with fractional spectral measures

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from σ when σ is in one of the classes of affine selfsimilar measures. Our analysis makes use of Kondratiev white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

态射的柱心-幂零分解

本文在正合加法范畴中研究了态射的Ｄｒａｚｉｎ逆,证明了态射的柱心－幂零分解的存在性和唯一性．     

A note on the mesh independence of convergence bounds for additive Schwarz preconditioned GMRES

Additive Schwarz preconditioners, when including a coarse grid correction, are said to be optimal for certain discretized partial differential equations, in the sense that bounds on the convergence of iterative methods are independent of the mesh size h. Cai and Zou (Numer. Linear Algebra Appl. 2002; 9 :379–397) showed with a one‐dimensional example that in the absence of a coarse grid correction the usual GMRES bound has a factor of the order of . In this paper we consider the same example and show that for that example the behavior of the method is not well represented by the above‐mentioned bound: We use an a posteriori bound for GMRES from (SIAM Rev. 2005; 47 :247–272) and show that for that example a relevant factor is bounded by a constant. Furthermore, for a sequence of meshes, the convergence curves for that one‐dimensional example, and for several two‐dimensional model problems, are very close to each other; thus, the number of preconditioned GMRES iterations needed for convergence for a prescribed tolerance remains almost constant. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Quasi-regularity of Semi-Dirichlet Forms

We prove that if a right Markov process is associated with a semi-Dirichlet form, then the form is necessarily quasi-regular. As applications, we develop the theory of Revuz measures in the semi-Dirichlet context and we show that quasi-regularity is invariant with respect to time change.     

基于分解测度的模糊积分及收敛定理(英文)

为了解决一些收敛定理 ,我们给出基于半环 ( [0 ,1 ], , )的伪可加分解测度的积分这种模糊积分被深入研究 .在给出这种积分的性质的基础上 ,我们得到一些收敛定理 ,它们是经典收敛定理的扩张 ,同时我们得到关于这种模糊测度的 Egorof定理     

量子随机Cable方程的白噪声分析方法

本文讨论了广义算子及其Wick积意义下的非线性量子随机Cable方程.在给出解的存在唯一性定理的基础上,证明了解对初值过程的连续依赖性及其他性质.     

在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。