Excursions of Markov Processes

I Markov Processes. - 0. Introduction. - 1. Basic terminology. - 2. Stationary transition functions. - 3. Time homogeneous Markov processes. - 4. The strong Markov property. - 5. Hitting times. - 6. Standard processes. - 7. Killed and stopped processes. - 8. Canonical realizations. - 9. Potential operators and resolvents. - II Examples. - 1. Examples. - 2. Brownian motion. - 3. Feller Brownian motions and related examples. - III Point Processes of Excursions. - 1. Additive processes. - 2. Poisson point processes. - 3. Poisson point processes of excursions. - IV Brownian Excursion. - 1. Brownian excursion. - 2. Path decomposition. - 3. The non-recurrent case. - 4. Feller Brownian motions. - 5. Reflecting Brownian motion. - V Itô's Synthesis Theorem. - 1. Introduction. - 2. Construction. - 3. Examples and complements. - 4. Existence and uniqueness. - 5. A counter-example. - 6. Integral representation. - VI Excursions and Local Time. - 1. Introduction. - 2. Ray's local time theorem. - 3. Trotter's theorem. - 4. Super Brownian motion. - VII Excursions Away From a Set. - 1. Introduction. - 2. Additive functionals and Lévy systems. - 3. Exit systems. - 4. Motoo Theory. - Notation Index. Language: English