Stochastic Functional Limit Theorems with Applications to Decision Making Under Uncertainty

摘要

A critical issue affecting the success of decision making is the underlying uncertainty. In this paper,we consider decision making problems involving uncertainties characterized by stochastic processes ofindependent stationary increments. The cost function of decision making is expressed as a functionof the decision time and associated values of stochastic processes. The decision time is a stoppingtime dependent on the parameters of decision rules. We investigate the asymptotic behavior of thecost function as the parameters of decision rules tend to certain values. We demonstrate that the costfunction follows stochastic functional limit theorems as the parameters of the decision rules tend tocertain values.