I reviewed the basics of Monte Carlo simulation and defined MSE and the bias–variance decomposition. Then I introduced the idea of importance sampling when working with probability densities.
I introduced the example of estimating the time to an event that occurs at a rate depending on an SDE. This motivated thinking about change of measure in path integrals and I discussed Girsanov’s theorem. I did not prove this, but gave a heuristic derivation.
I derived the Feynman-Kac formula and discussed the particle interpretation of path integrals.