Probability measures on graph trajectories
Michael J. Catanzaro, Vladimir Y. Chernyak, and John R. Klein
TL;DR
This paper constructs a probability measure on the space of trajectories for continuous-time Markov chains with finite or bounded degree state diagrams, filling a gap in the existing literature.
Contribution
It provides an elementary method to define probability measures on trajectories of Markov chains with finite or bounded degree, addressing a previously unfilled gap.
Findings
Defines probability measures on Markov chain trajectories
Applicable to chains with finite or bounded degree
Fills a gap in the theoretical literature
Abstract
The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is elementary. Our main intention is to fill a gap in the literature.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Markov Chains and Monte Carlo Methods · Quantum Mechanics and Applications