论文标题
部分可观测时空混沌系统的无模型预测
Most probable paths for developed processes
论文作者
论文摘要
仅针对特定过程（例如Riemannian Brownian运动）明确识别经典的Onsager-Machlup功能确定歧管点之间最可能的路径的最佳路径。这遗漏了大量的多种流动过程，例如具有平行运输的非平地扩散矩阵的过程，具有缺陷的生成器和亚右曼尼亚次数的过程，以及推送到商空间。在本文中，我们通过测量在此类过程的反开发方面的作用，构建了一种定义和识别最可能路径的定义和识别的通用方法。该构建包括大量的流动过程，并为大多数可能的路径带来显式方程系统。我们定义并得出这些结果，并将其应用于谎言组，均匀空间和形状分析中的地标空间上的几种随机过程。
Optimal paths for the classical Onsager-Machlup functional determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large classes of manifold-valued processes such as processes with parallel transported non-trivial diffusion matrix, processes with rank-deficient generator and sub-Riemannian processes, and push-forwards to quotient spaces. In this paper, we construct a general approach to definition and identification of most probable paths by measuring the Onsager-Machlup functional on the anti-developement of such processes. The construction encompasses large classes of manifold-valued process and results in explicit equation systems for most probable paths. We define and derive these results and apply them to several cases of stochastic processes on Lie groups, homogeneous spaces, and landmark spaces appearing in shape analysis.
