## STATS 310A: Theory of Probability I (MATH 230A)

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites:
STATS 116,
MATH 171.

Terms: Aut
| Units: 3

## STATS 310B: Theory of Probability II (MATH 230B)

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory. Prerequisite: 310A or
MATH 230A.

Terms: Win
| Units: 3

## STATS 310C: Theory of Probability III (MATH 230C)

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
http://statweb.stanford.edu/~adembo/stat-310c/

Terms: Spr
| Units: 3

Instructors:
Montanari, A. (PI)

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