Stochastic fundamental solutions for a class of degenerate SPDEs

In this thesis, we look for a fundamental solution for a broad, possibly degenerate class of stochastic partial differential equations (SPDEs), whose deterministic part is a Kolmogorov equation with coefficients measurable in the time variable. We use a version of the It\^o-Wentzell formula to reduce the SPDE to a PDE, for which we extend the classic Levi's parametrix method to find a fundamental solution