This Matlab code is related to our paper "Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models" published in SIAM Journal on Scientific Computing (click here to view the paper.) The paper is concerned with estimating unknown parameters in a continuous-time hidden Markov model (state space model). This code is used to generate Figure 5 in the published article for model 1. The code for the rest of models is very similar.
Let dx = dy = 1, dθ = 2 and consider the following linear SDE:
dXt = θ1 Xt dt + σ dWt
dYt = θ2 (κ - Xt) dt + dBt,
where {Wt}t>=0 and {Bt}t>=0 are two independent Brownian motions. κ and σ are both fixed and θ1, θ2 are the parameters to be inferred.