Title: Eigenfunctions Seminar: Basic law of large numbers and applications; Estimation of integrals with respect to infinite measures via RSMC
Speaker: K. B. Athreya (Professor Emeritus, Iowa State University, Ames, USA)
Date: 19 January 2018
Time: 3 - 5 pm
Venue: LH-1, Mathematics Department
Let X1 , X2 , X3,…Xn be iid random variables. Laws of large numbers roughly state that the average of these variables converges to the expectation value of each of them when n is large. Various forms of these laws have many applications. The strong and weak laws along with the following three applications will be discussed:
b) The Weierstrass approximation theorem.
c) The Glivenko–Cantelli theorem.
In the second half of this talk, a law of large numbers is proven for spaces with infinite “volume” (measure) as opposed to the above version for probability measures (“volume” =1).