Asymptotic stochastic programs. (English) Zbl 0847.90107

Pflug, Georg Ch.

Math. Oper. Res. 20, No. 4, 769-789 (1995).

Summary: Consider a stochastic program with unique solution. By the notion of epi-convergence in distribution in local coordinates, we define the asymptotic stochastic program associated to it. Stochastic programs may be classified according to the type of the pertaining asymptotic program. In particular, three such types are studied in detail: the normal shift program, the Wiener-type program and the Poisson-hyperplane program. Conditions for the convergence to each of the three types are given.

MSC:

90C15	Stochastic programming
62E20	Asymptotic distribution theory in statistics

Keywords:

unique solution; epi-convergence; asymptotic stochastic program; normal shift program; Wiener-type program; Poisson-hyperplane program