Communications in Mathematical Sciences
Volume 20 (2022)
Least squares estimation for delay McKean–Vlasov stochastic differential equations and interacting particle systems
Pages: 265 – 296
The aim of this paper is to solve the problem of parameter estimation for delay McKean–Vlasov stochastic differential equations (SDEs) with the coefficients exhibiting super-linear growth in the state component. Specifically, we propose a least squares estimator for an unknown parameter in the drift of a delay McKean–Vlasov SDEs with a small noise dispersion parameter by making use of time-discretized interacting particle systems and prove the weak convergence between the estimator and the true value, under suitable conditions. To achieve our main purposes on weak convergence, we give the approximation of the distribution of delay McKean–Vlasov SDEs at the discrete points and take advantage of calculating skills on the space of probability measures with finite order moments. Moreover, the asymptotic distribution of least squares estimator is derived via the properties of solutions for the corresponding interacting particle systems.
McKean–Vlasov SDE, interacting particle systems, discrete observation, least squares method, consistency of LSE, asymptotic distribution
2010 Mathematics Subject Classification
60G52, 60J75, 62F12, 62M05
This paper was supported by the National Natural Science Foundation of China (No. 11901188), and by the Scientific Research Funds of Hunan Provincial Education Department of China (No. 19B156).
Received 19 January 2021
Received revised 21 June 2021
Accepted 21 June 2021
Published 10 December 2021