Basics of Stochastic Automata Theory

Abstract

This chapter summarises results of the theory of stochastic automata. In Section 2.1, the stochastic automaton is defined and its representation by an automaton graph is explained. Mathematically, the stochastic automaton is a discrete stochastic processes. Its analysis, therefore, requires several notions and notations of stochastic processes that are introduced in Section 2.2. Based on this, the behaviour of stochastic automata is studied in Section 2.3. For the application of automata to fault diagnosis, the definition of the stochastic automaton is extended in Section 2.4. In Section 2.5 additional properties of automata like the stationary behaviour are discussed. Finally, in Section 2.6, stochastic operators are introduced and their relation to stochastic automata is shown.