Monte Carlo Optimization and Path Dependent Nonstationary Laws of Large Numbers
Abstract
New types of laws of large numbers are derived by using connections between estimation and stochastic optimization problems. They enable one to "track" time-and-path dependent functionals by using, in general, nonlinear estimators. Proofs are based on the new stochastic version of the Lyapunov's method. Applications to Monte Carlo optimization, stochastic branch and bounds method and minimization of risk functions are discussed.