Feynman-Kac formula

Let Xt be the n-dimensional Itō process satisfying the stochastic differential equation


and let A be its infinitesimal generator.

Further suppose that q is a lower-bounded continuous functionMathworldPlanetmath on n, and f is a twice-differentiable function on n with compact support. Then


is a solution to the partial differential equationMathworldPlanetmath


with initial conditionMathworldPlanetmath u(0,x)=f(x).

(The expectation for u is to be taken with respect to the probability measureMathworldPlanetmath under which Wt is a Brownian motionMathworldPlanetmath.)


  • 1 Bernt Øksendal. , An Introduction with Applications. 5th ed., Springer 1998.
  • 2 Hui-Hsiung Kuo. Introduction to Stochastic Integration. Springer 2006.
Title Feynman-Kac formula
Canonical name FeynmanKacFormula
Date of creation 2013-03-22 17:16:11
Last modified on 2013-03-22 17:16:11
Owner stevecheng (10074)
Last modified by stevecheng (10074)
Numerical id 6
Author stevecheng (10074)
Entry type Theorem
Classification msc 35K15
Classification msc 60H30
Classification msc 60H10
Related topic RichardFeynman