Theory of Markov Processes

PrefaceChapter 1 - Introduction 1. Measurable Spaces and Measurable Sets 2. Measures and Integrals 3. Conditional Probabilities and Mathematical Expectations 4. Topological Measurable Spaces 5. The Construction of Probability MeasuresChapter 2 - Markov Processes 1. The Definition of Markov Process 2. Stationary Markov Processes 3. Equivalent Markov ProcessesChapter 3 - Subprocesses 1. The Definition of Subprocess. The Connexion Between Subprocesses and Multiplicative functionals 2. Subprocesses Corresponding to Admissible Subsets. The Generation of a Part of a Process 3. Subprocesses Corresponding to Admissible Systems of Subsets 4. The Integral Type of Multiplicative Functionals and the Corresponding Subprocesses 5. Stationary Subprocesses of Stationary Markov ProcessesChapter 4 - The Construction of Markov Processes with Given Transition Functions 1. Definition of Transition Function. Examples 2. The Construction of Markov Processes with Given Transition Function 3. Stationary Transition Functions and the Corresponding Stationary Markov ProcessesChapter 5 - Strictly Markov Processes 1. Random Variables Independent of the Future and S-Past. Lemmas on Measurability 2. Definition of Strictly Markov Process 3. Stationary Strictly Markov Processes 4. Weakening the Form of the Condition for Processes continuous from the Right to be Strictly Markov 5. Strictly Markov Subprocesses 6. Criteria for a process to be Strictly MarkovChapter 6 - Conditions for Boundedness and Continuity of a Markov Process 1. Introduction 2. Conditions for Boundedness 3. Conditions for Continuity from the Right and Absence of Discontinuities of the Second Kind 4. Jump-Type and Step Processes 5. Continuity Conditions 6. A continuity Theorem for Strictly Markov Processes 7. ExamplesAddendum - A Theorem Regarding the Prolongation of Capacities, and the Properties of Measurability of the Instants of First Departure 1. A Theorem Regarding the Extension of Capacities 2. Measurability Theorems for the Instants of First DepartureSupplementary NotesReferencesAlphabetical IndexIndex of Lemmas and TheoremsIndex of Notation