Parameter Estimation for Partially Observed McKean-Vlasov Diffusions

arXiv (Cornell University)

Abstract

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of [5] we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation methodology. New Markov chain Monte Carlo algorithms for the POMV model are introduced facilitating the application of [5]. We prove, under assumptions, that the expectation of our estimator is biased, but with expected small and controllable bias. Our approach is implemented on several examples.

Authors 3

1. Ajay Jasra

   Chinese University of Hong Kong, Shenzhen

   Affiliation as printed

   School of Data Science , The Chinese University of Hong Kong , Shenzhen , Shenzhen , CN

2. Mohamed Maama

   King Abdullah University of Science and Technology · Computational Physics (United States)

   Affiliation as printed

   Applied Mathematics and Computational Science Program ,

   Computer, Electrical and Mathematical Sciences and Engineering Division , King Abdullah University of Science and Technology , Thuwal , 23955-6900 , KSA

3. Raul F. Tempone Aachen Chair of Mathematics for Uncertainty Quantification

   RWTH Aachen University · Computational Physics (United States)

   Affiliation as printed

   Applied Mathematics and Computational Science Program ,

   Chair of Mathematics for Uncertainty Quantification , RWTH Aachen University , 52062 Aachen , Germany