Conditions for deterministic limits of markov jump processes: The Kurtz theorem in chemistry

A theorem by Kurtz on convergence of Markov jump processes is presented as it relates to the use of the chemical master equation. Necessary mathematical background in the theory of stochastic processes is developed, as well as requirements of the mathematical model necessitated by results in the physical sciences. Applicability and usefulness of the master equation for this type of combinatorial model in chemistry is discussed, as well as analytical connections and modern applications in multiple research fields.