演講者：須上苑博士

單　位：中央研究院數學研究所

日　期：2011年5月4日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Optimal-reward problems on trees 

摘　要：

I will introduce some probabilistic problems on trees and some important results. Then we will focus on the optimal-reward problems: We assign i.i.d. random variables to the edges of a tree. We think of these random variables as rewards. For each path with length n, we sum up random variables along it. The optimal-reward at depth n is defined by taking the maximum of all those sums. I will present two results. The first one is the asymptotic behavior of the optimal-rewards. We consider that all edge weights are Gaussian. I will show that the asymptotic behavior of the optimal-rewards is close to their expectations, provided that the tree's growth has not been restrained. The other one for which all edge weights are not necessary Gaussian, we will show that the sooner the tree branches more, the greater the value of the optimal-reward.