### MA7880 Advanced Stochastic Processes

#### Course Details

Operator Semigroups: Hille-Yosida Theorem, Multivalued Operators, Semigroups on Function Spaces, Approximation and Perturbation Theorems. Stochastic Processes and Martingales: Local Martingales, Projection Theorem, Doob-Meyer Decomposition; Semigroups of Conditioned Shifts, Martingales indexed by directed sets. Convergence of probability measures, Prohorovâs Theorem, Generators and Markov Processes. Levy Processes, Levy-Khinchine Formulation, Stable Laws, Infinite divisibility.

#### Course References:

Text Books:

1. S. N..; Kurtz, T. G. Markov processes. Characterization and convergence. John Wiley & Sons, Inc., New York, 1986.

2. Stroock, D. W. Probability theory. An analytic view. Second edition. Cambridge University Press, Cambridge, 2011.

Reference Books:

1. Varadhan, S. R. S. Probability theory. Courant Lecture Notes in Mathematics, 7. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2001.

2. Dudley, R. M. Real analysis and probability. Revised reprint of the 1989 original. Cambridge Studies in Advanced Mathematics, 74. Cambridge University Press, Cambridge, 2002.

3. Billingsley, P. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999.

4. Billingsley, P. Probability and measure. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, 2012.