Pathwise numerics and dynamics of stochastic evolution equations

随机演化方程的路径数值和动力学

• 批准号: 29324846
• 负责人: Professor Dr. Peter E. Kloeden
• 金额: --
• 依托单位: Fachbereich 12 - Informatik und Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/29324846?language=en
• 关键词: Pathwise; numerics; dynamics; stochastic; evolution

Every finite dimensional Ito stochastic differential equation can be transformed into a pathwise random ordinary differential equation, which means that many dynamical properties can be investigated pathwise and numerical calculations can not only be carried out but also compared pathwise. The aim of this joint proposal is to investigate if such a pathwise equivalence also holds for stochastic evolution equations, in particular for semilinear parabolic stochastic partial differential equations and to exploit it in the context of dynamics and numerics.

每个有限维的Ito随机微分方程都可以转化为路径随机常微分方程，这意味着许多动力学性质可以路径地研究，数值计算不仅可以进行路径比较，而且还可以进行路径比较。这个联合方案的目的是研究这种路径等价是否也适用于随机发展方程，特别是半线性抛物型随机偏微分方程组，并在动力学和数值的背景下利用它。

项目成果

Inertial manifolds for stochastic pde with dynamical boundary conditions

• DOI: 10.3934/cpaa.2011.10.831
• 发表时间: 2010-12
• 期刊: Communications on Pure and Applied Analysis
• 影响因子: 1
• 作者: Peter Brune;B. Schmalfuß

Ergodicity of the Infinite Dimensional Fractional Brownian Motion

• DOI: 10.1007/s10884-011-9222-5
• 发表时间: 2011-09-01
• 期刊: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
• 影响因子: 1.3
• 作者: Garrido-Atienza, Maria J.;Schmalfuss, Bjoern
• 通讯作者: Schmalfuss, Bjoern

Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions

• DOI: 10.1080/07362990902976546
• 发表时间: 2009-08
• 期刊: Stochastic Analysis and Applications
• 影响因子: 1.3
• 作者: Peter Brune;Jinqiao Duan;B. Schmalfuß

Global attractor for a non-autonomous integro-differential equation in materials with memory

• DOI: 10.1016/j.na.2010.03.012
• 发表时间: 2010-07
• 期刊: Nonlinear Analysis-theory Methods & Applications
• 影响因子: 1.4
• 作者: T. Caraballo;M. Garrido-Atienza;B. Schmalfuß;J. Valero

RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

• DOI: 10.1142/s0218127410027349
• 发表时间: 2010-09-01
• 期刊: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
• 影响因子: 2.2
• 作者: Garrido-Atienza, M. J.;Maslowski, B.;Schmalfuss, B.
• 通讯作者: Schmalfuss, B.