Dr. Krishna B. Athreya, emeritus distinguished professor of mathematics at Iowa State University, will present two open lectures at S&T. The first, titled “Measure Theory Model for Studying Randomness Time,” will be held at 4:15 p.m. today, Thursday March 20, in Room G-5 Rolla Building. Refreshments will be served at 4 p.m. All Missouri S&T students, faculty and staff are invited to attend both lectures.

At 4:15 p.m. Friday, March 21, in Room G-5 Rolla Building, Athreya will present “Monte Carlo Methods for Improper Targets Time.” Refreshments will be served at 4 p.m.

Athreya is internationally known for his work in probability theory, stochastic processes, mathematical statistics and stochastic modeling and applications. To see a list of upcoming lectures from the S&T mathematics and statistics department, visit its lecture schedule.

Abstract for Thursday’s lecture: “The real world has both deterministic and random phenomenon. To study the later mathematically a useful tool is measure theory. We will explain this approach due to A.N. Kolmogorov and illustrate this with the cases when the phenomenon has i) finite number of outcomes ii) countable number of outcomes and iii) uncountable number of outcomes iv) functions over an interval as outcome.”

Abstract of Friday’s lecture: “Let f be an integrable function on a measure space where the measure of the whole space is infinite. Consider the problem of estimating the integral of f over this space. The usual MCMC or iid sampling will not work here. It will be shown that if a regenerative sequence of random variables could be generated with the given measure as its canonical measure then a consistent estimator can be found. Further if the regeneration time has a regularly varying tail and f has an appropriate second moment then a central limit theorem will also be established. This can be used to get confidence intervals. All of this will be illustrated with counting measure on the integers with a simple symmetric random walk.”