Robustness in Stochastic Filtering and Maximum Likelihood Estimation for SDEs

Approximate Likelihood Construction for Rough Differential Equations

“…We have already seen that D c F θ 0 is given by the process Z(c) defined in (8). So, the above relationship becomes ∆x i − ∆x i = Z(ξ i ) −1 y t i+1 − F θ 0 (y t i , δ; ∆x i ) .…”

“…Clearly, in this case, the solution of system (6) always exists and is unique under the condition that σ = 0. Let us now compute the process Z defined in (8). In this case, since d = 1, this is a scalar process.…”

“…Bayesian inference is conducted in the article [25] where rough paths approach is adopted and data augmentation technique and Hybrid Monte Carlo are employed. Stochastic filtering and MLEs in rough paths setting are investigated in [8] and related papers [6], [9], [7].…”