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.
翻译:我们开发了一种可测有效的重要取样方案, 估计从稳定平衡的相邻区域缩放小噪音蒸汽反扩散方程式的解决方案退出概率。 中度偏差缩放使非线性动态可以通过线性版本在当地近似。 此外, 我们确定出出口发生概率高的有限维次空间 。 使用随机控制和变异方法, 我们显示我们的方案在零噪声限制和静默前两个方面都表现良好。 模拟随机近距离双曲线动态研究显示了理论结果 。