Speaker : | Prof. Krishina B. Athreya (Iowa State University) |
Title : | 1. Coalescence in critical and subcritical Galton Watson processes 2. Staistical estimation of integrals w.r.t. infinite measures |
Time : | 2014-06-09 (Mon) 14:10 - 16:30 |
Place : | Seminar Room 617, Institute of Mathematics (NTU Campus) |
Abstract: | 1.If a Galton Watson process is not extinct by the nth generation and has at least two individuals, pick two individuals at random by SRSWOR. Trace their lines of descent back in time till they meet. Call that generation Xn a pairwise coalescence time. Let Yn denote the coalescence time for the whole population of the nth generation conditined on non extinction. In this talk we present results on the limit behaviors of Xn and Yn for both critical and subcritical cases. 2. Let f be an integrable function on an infinite measure space, the usual MCMC or iid Monte Carlo will not work here. We show that if a regenerative sequence with the given measure as its canonical measure could be generated then a consistent estimation is possible. Under some appropriate conditions a confidence interval also can be constructed. This is all illustrated with estimating countable sums and integrals w.r.t. Lebesgue measure on Rd using SSRW. |