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ERGODICITY OF REGIME-SWITCHING FUNCTIONAL DIFFUSIONS WITH INFINITE DELAY AND APPLICATION TO A NUMERICAL ALGORITHM FOR STOCHASTIC OPTIMIZATION.
- Source :
-
SIAM Journal on Control & Optimization . 2022, Vol. 60 Issue 5, p2658-2683. 26p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03630129
- Volume :
- 60
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Control & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 159825075
- Full Text :
- https://doi.org/10.1137/22M1470050