The Theory of Stochastic Processes II

I. Basic Definitions and Properties of Markov Processes.- § 1. Wide-Sense Markov Processes.- § 2. Markov Random Functions.- § 3. Markov Processes.- § 4. Strong Markov Process.- § 5. Multiplicative Functional.- § 6. Properties of Sample Functions of Markov Processes.- II. Homogeneous Markov Processes.- § 1. Basic Definitions.- § 2. The Resolvent and the Generating Operator of a Weakly Measurable Markov Process.- § 3. Stochastically Continuous Processes.- § 4. Feller Processes in Locally Compact Spaces.- § 5. Strong Markov Processes in Locally Compact Spaces.- § 6. Multiplicative Additive Functionals, Excessive Functions.- III. Jump Processes.- § 1. General Definitions and Properties of Jump Processes.- § 2. Homogeneous Markov Processes with a Countable Set of States.- § 3. Semi-Markov Processes.- § 4. Markov Processes with a Discrete Component.- IV. Processes with Independent Increments.- §1. Definitions. General Properties.- § 2. Homogeneous Processes with Independent Movements. One-Dimensional Case.- § 3. Properties of Sample Functions of Homogeneous Processes with Independent Increments in ?1.- §4. Finite-Dimensional Homogeneous Processes with Independent Increments.- V. Branching Processes.- § 1. Branching Processes with Finite Number of Particles.- § 2. Branching Processes with a Continuum of States.- §3. General Markov Processes with Branching.- Historical and Bibliographical Remarks.