El. knyga: Continuous Parameter Markov Processes and Stochastic Differential Equations

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. Itō'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.

Rabi Bhattacharya is Professor of Mathematics at The University of Arizona. He is a Fellow of the Institute of Mathematical Statistics and a recipient of the U.S. Senior Scientist Humboldt Award and of a Guggenheim Fellowship. He has made significant contributions to the theory and application of Markov processes, and more recently, nonparametric statistical inference on manifolds. He has served on editorial boards of many international journals and has published several research monographs and graduate texts on probability and statistics. Edward C. Waymire is Emeritus Professor of Mathematics at Oregon State University. He received a PhD in mathematics from the University of Arizona in the theory of interacting particle systems. His primary research concerns applications of probability and stochastic processes to problems of contemporary applied mathematics pertaining to various types of flows, dispersion, and random disorder. He is a formerchief editor of the Annals of Applied Probability, and past president of the Bernoulli Society for Mathematical Statistics and Probability.