In this work, we generalize the concept of bisimulation metric in order to metrize the behaviour of continuous-time processes. Similarly to what is done for discrete-time systems, we follow two approaches and show that they coincide: as a fixpoint of a functional and through a real-valued logic. The whole discrete-time approach relies entirely on the step-based dynamics: the process jumps from state to state. We define a behavioural pseudometric for processes that evolve continuously through time, such as Brownian motion or involve jumps or both.

翻译：在本工作中，我们推广了互模拟度量的概念，以度量连续时间过程的行为。类似于离散时间系统的处理方法，我们遵循两种途径并证明它们是一致的：作为泛函的不动点，以及通过实值逻辑。整个离散时间方法完全依赖于基于步长的动态：过程从一个状态跳转到另一个状态。我们为在时间上连续演化的过程（如布朗运动）、涉及跳跃的过程或两者兼有的过程定义了一种行为伪度量。