Bisimulation for Feller-Dynkin Processes

TL;DR

This paper introduces two equivalent definitions of bisimulation for continuous-time stochastic processes, extending the concept from discrete-time systems and emphasizing the flow of evolution through time.

Contribution

It proposes a novel bisimulation framework for continuous-time processes that generalizes and unifies existing discrete-time concepts.

Findings

The two bisimulation definitions are shown to be equivalent.

The new bisimulation encompasses standard discrete-time bisimulation as a special case.

The concept is not a simple extension but a distinct generalization.

Abstract

Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is continuous but the evolution still proceeds in jumps. We propose two definitions of bisimulation on continuous-time stochastic processes where the evolution is a \emph{flow} through time. We show that they are equivalent and we show that when restricted to discrete-time, our concept of bisimulation encompasses the standard discrete-time concept. The concept we introduce is not a straightforward generalization of discrete-time concepts.