Abstract
It is well known that ergodicity and the strong law of large numbers (SLLN) play important roles in stochastic control and stochastic approximations. For a class of regime-switching functional diffusion processes with infinite delay, this paper establishes exponential ergodicity in a Wasserstein distance under certain “averaging conditions.” It follows from such an ergodicity property that an SLLN for additive functionals of the regime-switching diffusions is obtained based on the property of uniform mixing. Finally, an example is presented to illustrate the application of ergodicity and the SLLN to a numerical algorithm for stochastic optimization.
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