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Eigenfunctions Seminar

Title: Basic law of large numbers and applications; Estimation of integrals with respect to infinite measures via RSMC
Speaker: Krishna B. Athreya (Professor Emeritus, Iowa State University, Ames, USA)
Date: 19 January 2018
Time: 3 – 5 pm (with a 15 minute break in between)
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: a) Coin-tossing. 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).

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 May 2024