Examples
This section shows runnable TME examples in Python and Matlab. In particular, we use the following two example models.
Model 1,
\[d X(t) = \mathrm{tanh}(X(t)) dt + dW(t).\]Model 2,
\[\begin{split}d X_1(t) &= X_2(t), \\ d X_2(t) &= (X_1(t)\, (\kappa - (X_1(t))^2)) dt + X_1(t) dW(t).\end{split}\]
We want to compute their mean, covariance/variance, or more generally \(\mathbb{E}[\phi(X(t + \Delta t)) \mid X(t)]\) for any function of interest \(\phi\).
In Python
See, Jupyter Notebook (SymPy) for Model 1.
See, Jupyter Notebook (JaX) for Model 1.