论文标题
作为广义梯度流动的跳跃过程
Jump processes as Generalized Gradient Flows
论文作者
论文摘要
我们为一类非金属梯度系统创建了功能框架。状态空间是非负措施的空间，并且系统类别包括向波兰空间上马尔可夫跳跃过程定律的前向kolmogorov方程。该框架包括一个解决方案概念的定义，一种证明存在的方法以及原型唯一性结果。我们仅使用耗散功能直接提供的结构来做到这一点，而耗散功能不必均匀，并且我们不吸引任何度量结构。
We have created a functional framework for a class of non-metric gradient systems. The state space is a space of nonnegative measures, and the class of systems includes the Forward Kolmogorov equations for the laws of Markov jump processes on Polish spaces. This framework comprises a definition of a notion of solutions, a method to prove existence, and an archetype uniqueness result. We do this by using only the structure that is provided directly by the dissipation functional, which need not be homogeneous, and we do not appeal to any metric structure.
