Author | Blumenthal, Robert M. author |
---|---|
Title | Excursions of Markov Processes [electronic resource] / by Robert M. Blumenthal |
Imprint | Boston, MA : Birkhรคuser Boston, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9412-9 |
Descript | XII, 276 p. online resource |
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 Itรดโs 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. Rayโs local time theorem -- 3. Trotterโs theorem -- 4. Super Brownian motion -- VII Excursions Away From a Set -- 1. Introduction -- 2. Additive functionals and Lรฉvy systems -- 3. Exit systems -- 4. Motoo Theory -- Notation Index