论文标题
中等偏差方程的随机反应扩散方程的重要性采样
Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime
论文作者
论文摘要
我们开发了一种非常有效的重要性抽样方案，该方案估计了从稳定平衡的缩放邻域中估计解决方案的溶液的退出概率。中等偏差缩放允许通过线性化版本对非线性动力学进行局部近似。此外，我们确定一个有限维的子空间，在该子空间中出现很高的可能性。使用随机控制和变异方法，我们表明我们的方案在零噪声限制和预先质量上都表现良好。随机扰动的双态动力学的模拟研究说明了理论结果。
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation scaling allows for a local approximation of the nonlinear dynamics by their linearized version. In addition, we identify a finite-dimensional subspace where exits take place with high probability. Using stochastic control and variational methods we show that our scheme performs well both in the zero noise limit and pre-asymptotically. Simulation studies for stochastically perturbed bistable dynamics illustrate the theoretical results.
