Inference on SDE's


A stochastic differential equation describes the change in some variable, $X$, at a given time, $t$.

\[d X_t = \mu(X_{t-1}, \theta) dt + \sigma(X_{t-1}, \theta) dW_t\]

Why is inference hard?

  • The likelihood is intractable: We cannot write down the likelihood. This makes maximum likehood inference nearly impossible, and