MATH 289A: TOPICS IN PROBABILITY (FALL 2008)
  • Lecture 1-2: Introduction
  • Lectures 3-5: Path Space, Weak Convergence of Stochastic Processes
  • Lecture 4: Notes from October 20, 2008, taken by Allison Cutler.
  • Lecture 5: Notes from October 22, 2008, taken by Feng Liu.
  • Lecture 6: Start of Biochemical Reaction Networks -- notes from October 27, 2008, taken by Chris Chang.
  • Lecture 7: Fluid limits of Biochemical reaction networks -- notes from October 29, 2008, taken by Alex Bilik. Beware, this is a large file (in megabytes). A typed verson of the notes is available here.
  • Lecture 8: Fluid limit justification with mass action kinetics.
  • Lecture 9: Complex balance equilibrium and connection to product form stationary distributions. (Decomposition of RHS of ode in form YA Psi. For a mathematica notebook to do this automatically, click here.)
  • Schedule of Presentations by Students.
    1. Skorokhod Representation Theorem: Allison Cutler, Friday, October 31, noon-12.50pm.
    (Some notes on the web by Borkar relating to the Skorokhod space.)
    2. Central limit theorem for heavy tails: Chris Chang and Alex Bilik, Friday, November 14, 2008, noon-12.50p.m.
    3. Ode models in biochemistry: Bo Hu and Wen Chen, November 21, 2008, noon-1pm.
    3. M1 topology: Michael Kinnally
    4. Skorokhod problem: Teng Gao
    5. Diffusion approximation for a two-user downlink system in heavy traffic: Raghava Swamy.
    6. Strong approximations for Markovian service systems: Vladimir Pesic.
    7. Stolyar's maxweight paper: Abhijeet Bhorkar.