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" Probability Bounds via Stochastic Dynamic Programming with applications to Reliability " In this talk we indicate how many probability inequalities can be derived via stochastic dynamic programming type arguments, by setting up the problem as a game against "nature". In particular, we show how to use such an approach to find tight bounds on the Renewal function under specified nonparametric restrictions on the distribution driving the renewal process. Such bounds are useful since closed form expressions are generally not known for most renewal processes. Interpretations of some of our bounds are provided in a reliability application context of repairable systems. |