Abstract:

In this paper we give an estimation of the parameters of the stationary distribution of some mean field diffusion process using the differential equations of that distribution. The mean field stochastic process involved is dX(t)=b(μ^N,θ)dt+σ(X(t))dB(t), where θ is parameters to be estimated. μ^N is the empirical distribution of the N subjects consisting the mean field stochastic process. b(μ,θ) is continuous wrt μ at μ=p(τ-topology). Where p is the unique stationary distribution of the process. We restrict ourself to the study of the parameter estimation problem of the following model dX(t)=(aθ(X(t))+b<F,μ(t)>)dt+σ(X(t))dB(t), where a,b are parameters to be estimated. The data is the empirical distribution of large amount of subjects consisting the process on several time points.

Key words: Meanfield stochastic process, Kolmogorov forward equation, Parameter estimation