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Math 672 —
Spring 2001
Stochastic Processes
| Instructor: |
Eugene Dynkin |
| Time: |
TR 10:10–11:25 |
| Room: |
MT 206 |
- Theory of stochastic interaction (conditional independence,Gibbs formula,Markov
fields on graphs, Ising model-thermodynamic limit, Gaussian fields)
- Markov chains in a general measurable state space, asymptotic behavior
at large time ( ergodicity coefficient, weak and strong ergodicity),
the case of a finite and countable state space, random walks. Stopping
times, strong Markov property, Doeblin's method, renewal theorem.
- Brownian motion (passage to the limit from random walks, construction
of continuous Brownian motion, invariance and self-similarity properties,
first exit times and exit distributions, Markov and strong Markov properties,
Blumenthal's 0-1 law,probabilistic solution of the Dirichletr problem).
- Martingales (the Doob-Meyer decomposition, Doob's upcrossing inequality,
Kolmogorov's inequality, Hilbert space of continuous martingales). Stochastic
integrals, stochastic differential equations, Ito's formula, diffusions.
Last modified:
April 7, 2003
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