The Heston's PDE is a variable coefficient linear PDE. I know the existence of fundamental solution of constant coefficient linear PDE has been proofed by Bernard Malgrange and Leon Ehrenpreis in 1954 already. However, I didn't find any proof of the variable coefficient ones. My questions are like this:
- How can I know whether such a fundamental solution of Heston's PDE exist or not.
- If I cannot know the former question for sure. How about if I have got a semi-analytical solution. That is, can I judge the existence of the fundamental solution by the solution I have got.