STAT 206A - Fall
2004
Stochastic Processes
Instructor: Steven N.
Evans
Time and Place: TT 11:00-12:30, 332 Evans Hall
Instructor Office: 329 Evans Hall
Instructor Phone: 1-510-642-2777
Instructor e-mail: evans@stat.berkeley.edu
Office Hours: by appointment
Text: Slides from class available in PDF here
or in a more compressed form (several slides to a page) here
Course Description: I will be looking at interconnections
between Markov
processes, metric geometry, "fractal" geometry, and random trees.
- uniform
random trees and conditioned Galton-Watson
branching processes
- matrix-tree
theorem
- Aldous-Broder algorithm and Wilson algorithm for simulating random trees
- Harris
paths, connections between random trees and random walks
- Ito
excursion theory
- continuum
random tree
- metric
geometry, Hausdorff distance, Gromov-Hausdorff distance
- real
trees and lambda trees
- Markov
processes, Hille-Yosida theory, Feller
processes
- Markov
processes on tree space
- Dirichlet forms, potential theory
- more
Markov processes on tree space
- Hausdorff measure, Hausdorff
dimension, capacity
- Kingman's
coalescent
- coalescing
Brownian motion, Arratia flow, sticky flows
- snakes
and spiders, Martin compactification,
Martin boundary, stochastic calculus
- pinching
and twisting, processes on stratified and vermiculated spaces