Limit theorems for additive functionals of path-dependent SDEs

Jianhai Bao, ,Center for Applied Mathematics, Tianjin University, Tianjin 300072, China, Feng-Yu Wang, Chenggui Yuan, ,Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, UK
2020 Discrete and Continuous Dynamical Systems. Series A  
By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations. 2020 Mathematics Subject Classification. Primary: 34K50, 37A30; Secondary: 60J05. Key words and phrases. Strong law of large numbers, central limit theorem, law of iterated logarithm, ergodicity, path-dependent SDEs.
doi:10.3934/dcds.2020224 fatcat:qif7emwk4vewrp4234rpywp6ne