Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Bisimulation through probabilistic testing
Information and Computation
Probability
Bisimulation for Labelled Markov Processes
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Logical Characterization of Bisimulation for Labeled Markov Processes
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Semi-pullbacks for stochastic relations over analytic spaces
Mathematical Structures in Computer Science
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Tracing Relations Probabilistically
Fundamenta Informaticae
Tracing Relations Probabilistically
Fundamenta Informaticae
A computable approach to measure and integration theory
Information and Computation
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
The converse of a stochastic relation
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Semi-pullbacks and bisimulations in categories of stochastic relations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Coalgebraic logic over general measurable spaces ??? a survey
Mathematical Structures in Computer Science
Unprovability of the logical characterization of bisimulation
Information and Computation
A characterization of meaningful schedulers for continuous-time markov decision processes
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Bisimulation for general stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Tracing Relations Probabilistically
Fundamenta Informaticae
Tracing Relations Probabilistically
Fundamenta Informaticae
Approximating Markov Processes by Averaging
Journal of the ACM (JACM)
Hi-index | 0.00 |
We show that the category whose objects are families of Markov processes on Polish spaces, with a given transition kernel, and whose morphisms are transition probability preserving, surjective continuous maps has semi-pullbacks, i.e., for any pair of morphisms f i:S i→S (i = 1, 2), there exists an object V and morphisms π i:V→S i (i = 1, 2) such that f 1∘π 1 = f 2∘π 2. This property holds for various full subcategories, including that of families of Markov processes on locally compact second countable spaces, and in the larger category where the objects are families of Markov processes on analytic spaces and morphisms are transition probability preserving surjective Borel maps. It also follows that the category of probability measures on Polish spaces and measure-preserving continuous surjective maps has semi-pullbacks. A main consequence of our result is that probabilistic bisimulation for labelled Markov processes on all these categories, defined in terms of spans of morphisms, is an equivalence relation.