用Onsager-Machlup函数作为跳扩散过程最可能路径的拉格朗日量
The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Jump-diffusion Process
摘要：
本文研究了一类随机动力系统在（非高斯）Levy噪声和（高斯）Brownian噪声下的Onsager-Machlup函数，并研究了相应的最可几路径.该Onsager-Machlup函数是给出跳跃扩散过程的连接亚稳态的最可能路径的拉格朗日函数。这是通过应用Girsanov变换引起的跳跃扩散过程的措施。此外，我们还发现，在扩散过程的特殊情况下，这个拉格朗日函数与结果是一致的。最后，我们应用这个新的Onsager-Machlup函数来研究几个例子中的动力学行为的解析和数值。这些包括从一个亚稳态的过渡到另一个亚稳态在双阱系统中，与数值实验说明了最可能的过渡路径的各种噪声参数。
英文摘要：
This work is devoted to deriving the Onsager-Machlup function for a class of stochastic dynamical systems under (non-Gaussian) Levy noise as well as (Gaussian) Brownian noise, and examining the corresponding most probable paths. This Onsager-Machlup function is the Lagrangian giving the most probable path connecting metastable states for jump-diffusion processes. This is done by applying the Girsanov transformation for measures induced by jump-diffusion processes. Moreover, we have found this Lagrangian function is consistent with the result in the special case of diffusion processes. Finally, we apply this new Onsager-Machlup function to investigate dynamical behaviors analytically and numerically in several examples. These include the transitions from one metastable state to another metastable state in a double-well system, with numerical experiments illustrating most probable transition paths for various noise parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
