New version of optimal stopping problem

This dissertation contains several new results concerning Moser-type optimal stopping problems. In the simplest case we consider sequence of independent uniformly distributed points X1, X2, · · · , Xn on the compact Riemannian manifold M and give algorithm for the calculation of Sn = maxτ≤nE[G(Xτ )]where G is a smooth function on M and τ is a random optimal stopping time. Description of the optimal τ depends on the structure of G near points of maximum. For different assumptions on this structure we calculate asymptotics of Sn.