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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

21 votes
3 answers
6k views

Why pi-systems and Dynkin/lambda systems? On the relative merits of approaches in measure th...

What is the point of $\pi$-systems and $\mathcal{D}$ / Dynkin / $\lambda$-systems? I am an analyst in the process of consolidating my measure theory knowledge before moving on to harder/newe …
11 votes
5 answers
4k views

Brownian motion, martingales, Markov Chains - Rosetta Stone

What are the most fundamental/useful/interesting ways in which the concepts of Brownian motion, martingales and markov chains are related? I'm a graduate student doing a crash course in p …