论文标题
Kunita SDE的最可能流量
Most probable flows for Kunita SDEs
论文作者
论文摘要
我们确定了Kunita Brownian动作的最可能的流动，即具有Eulerian噪声和确定性漂移的随机流。这样的随机过程例如在流体动力学和形状分析中出现，以粗略确定性动力学以及细粒度的噪声进行建模。我们通过为基础域配备源自噪声的riemannian度量来处理这个无限的维度问题。通过将方程与各种噪声结构选择整合在一起，将最大可能的流量与非扰动的确定性流程进行了比较。
We identify most probable flows for Kunita Brownian motions, i.e. stochastic flows with Eulerian noise and deterministic drifts. Such stochastic processes appear for example in fluid dynamics and shape analysis modelling coarse scale deterministic dynamics together with fine-grained noise. We treat this infinite dimensional problem by equipping the underlying domain with a Riemannian metric originating from the noise. The resulting most probable flows are compared with the non-perturbed deterministic flow, both analytically and experimentally by integrating the equations with various choice of noise structures.
