Continuous Parameter Markov Processes and Stochastic Differential Equations (Paperback)

1. A review of Martingaels, stopping times and the Markov property.- 2. Semigroup theory and Markov processes.-3. Regularity of Markov process sample paths.- 4. Continuous parameter jump Markov processes.- 5. Processes with independent increments.- 6. The stochastic integral.- 7. Construction of difficusions as solutions of stochastic differential equations.- 8. Ito's Lemma.- 9. Cameron-Martin-Girsanov theorem.- 10. Support of nonsingular diffusions.- 11. Transience and recurrence of multidimensional diffusions.- 12. Criteria for explosion.- 13. Absorption, reflection and other transformations of Markov processes.- 14. The speed of convergence to equilibrium of discrete parameter Markov processes and Diffusions.- 15. Probabilistic representation of solutions to certain PDEs.- 16. Probabilistic solution of the classical Dirichlet problem.- 17. The functional Central Limit Theorem for ergodic Markov?processes.- 18. Asymptotic stability for singular diffusions.- 19. Stochastic integrals with L2-Martingales.- 20. Local time for Brownian motion.- 21. Construction of one dimensional diffusions by Semigroups.- 22. Eigenfunction expansions of transition probabilities for one-dimensional diffusions.- 23. Special Topic: The Martingale Problem.- 24. Special topic: multiphase homogenization for transport in periodic media.- 25. Special topic: skew random walk and skew Brownian?motion.- 26. Special topic: piecewise deterministic Markov processes in population biology.- A. The Hille-Yosida theorem and closed graph theorem.- References.- Related textbooks and monographs.