A behavioural pseudometric for continuous-time Markov processes

Linan Chen; Florence Clerc; Prakash Panangaden

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arXiv · 2501.13008

A behavioural pseudometric for continuous-time Markov processes

Linan Chen·Florence Clerc·Prakash Panangaden

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Abstract

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.

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Linan Chen, Florence Clerc, Prakash Panangaden. 2025-01-22. A behavioural pseudometric for continuous-time Markov processes. https://arxiv.org/abs/2501.13008

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