Martingales in discrete and continuous time, Brownian Motion, Sample path properties, predictable processes, stochastic integrals with respect to Brownian motion and semimartingales, stochastic differential equations. Applications mostly to counting processes and finance. Knowledge of measure-theoretic probability at the level of Statistics 600 is a prerequisite for the course, although some key concepts, such as conditioning, are reviewed. After Statistics 600. |
Instructor: | David Pollard (email: david.pollard@yale.edu) |
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Office hours: | to be announced |
Time: | Friday 1:30 -- 3:30 plus weekly meetings with DP (see email.3sept04.txt for details) |
Place: | 24 Hillhouse |
TA: | Stephan Winkler |
My aim is to explain enough theory to give students an understanding of the calculus of stochastic integration with respect to semimartingales.