NUMERICS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

抛物型随机偏微分方程的数值模拟

• 批准号: EP/D049792/1
• 负责人: Michael Tretyakov
• 金额: $ 10.32万
• 依托单位: University of Leicester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD049792%2F1
• 关键词: NUMERICS; STOCHASTIC; PARTIAL; DIFFERENTIAL; EQUATIONS

Stochastic partial differential equations (SPDEs) are an essential tool in the description of complex systems affected by external or internal fluctuations arising in physics, chemistry, biology, finance. Effective numerical methods play crucial role in studying models described by SPDEs. Numerics for SPDEs is a relatively new area of stochastic numerical analysis and its further development is essential for both practice and theory. We well know how it is important to have a large arsenal of methods for deterministic equations. This is even more important in the case of SPDEs due to their higher complexity. The proposed research will develop the new approach to numerics for SPDEs and give new methods together with their rigorous analysis using novel ideas of layer methods. The proposed methods will be tested on model problems.

随机偏微分方程（SPDEs）是描述物理、化学、生物、金融等领域受外部或内部波动影响的复杂系统的重要工具。有效的数值方法对于研究spde描述的模型至关重要。SPDEs数值是随机数值分析的一个相对较新的领域，它的进一步发展对实践和理论都有重要意义。我们都知道，对于确定性方程，拥有大量的方法库是多么重要。这在spde的情况下更为重要，因为它们的复杂性更高。提出的研究将开发新的spde数值方法，并使用新颖的层方法思想对其进行严格的分析，给出新的方法。提出的方法将在模型问题上进行测试。

项目成果

Numerical solution of the Dirichlet problem for linear parabolic SPDEs based on averaging over characteristics

基于平均特性的线性抛物型 SPDE 狄利克雷问题的数值求解

• 发表时间: 2011
• 作者: V Stanciulescu

Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations

• DOI: 10.1137/090770527
• 发表时间: 2009-08
• 期刊: SIAM J. Numer. Anal.
• 作者: Jonathan C. Mattingly;A. Stuart;M. Tretyakov

Practical Variance Reduction via Regression for Simulating Diffusions

通过模拟扩散的回归来减少实际方差

• DOI: 10.1137/060674661
• 发表时间: 2009
• 期刊: SIAM Journal on Numerical Analysis
• 影响因子: 2.9
• 作者: Milstein G

Monte Carlo methods for backward equations in nonlinear filtering

非线性滤波中后向方程的蒙特卡罗方法

• DOI: 10.1239/aap/1240319577
• 发表时间: 2016
• 期刊: Advances in Applied Probability
• 影响因子: 1.2
• 作者: Milstein G