Akshay Balsubramani (Theory Seminar S15)

balsubramani.jpg"Non-Asymptotic Extensions to the Law of the Iterated Logarithm"
Akshay Balsubramani
Monday, May 11th, 2015, 2:00 pm
EBU3B, Room 4258
We give concentration bounds for martingales, a broad generalization of random walks, that are uniform over all finite times and extend classical Hoeffding and Bernstein bounds. With small changes to the method of proof, we prove a novel matching anti-concentration inequality showing our results to be optimal in a strong sense. Other extensions include uniform concentration of martingale mixtures. The new inequalities and their method of proof offer insights into the relationship between the central limit theorem and the law of the iterated logarithm in finite time.