Feynman-Kac formula

introduction

• The classical Feynman-Kac formula states the connection between
  • linear parabolic partial differential equations (PDEs), like the heat equation, and
  • expectation of stochastic processes driven by Brownian motion
• It gives then a method for solving linear PDEs by Monte Carlo simulations of random processes

memo

• One possible source is the book of Brian Hall on quantum mechanics for mathematicians.
• Another possibility is the series on functional analysis by Reed and Simon
• Fokker–Planck equation

articles

• Pham, Huyen. “Feynman-Kac Representation of Fully Nonlinear PDEs and Applications.” arXiv:1409.0625 [math], September 2, 2014. http://arxiv.org/abs/1409.0625.

Feynman diagrams and path integral