Alladi Ramakrishnan Hall

Statistical Estimation of integrals w.r.t infinite measures

K. B. Athreya

Iowa State University

The law of large numbers and the central limit theorem yield methods to estimate integrals w.r.t. probability measures. This is now called IID MonteCarlo (IIDMC).For the last 25  years another method known as MCMC has become
popular. Neither works for infinite measures. In this talk we show how regenerative stochastic sequences and processes can be used to solve this problem. We call this method RSMC.We illustrate this with the use of SSRW(simple symmetric random walk on Z) and standard Brownian motion on R.