We derive a path-kernel formula for the linear response of SDEs, where the perturbation applies to initial conditions, drift coefficients, and diffusion coefficients. It tempers the unstableness by gradually moving the path-perturbation to hit the probability kernel. Then we derive a pathwise sampling algorithm and demonstrate it on the Lorenz 96 system with noise.

翻译：我们推导了随机微分方程线性响应的路径核公式，其中扰动作用于初始条件、漂移系数和扩散系数。该方法通过逐渐移动路径扰动以触及概率核，从而缓和了不稳定性。随后我们推导了路径采样算法，并在带噪声的Lorenz 96系统上进行了验证。