Feynman-Kac formula
Let be the -dimensional Itō process satisfying the stochastic differential equation
and let be its infinitesimal generator.
Further suppose that is a lower-bounded continuous function on , and is a twice-differentiable function on with compact support. Then
is a solution to the partial differential equation
with initial condition .
(The expectation for is to be taken with respect to the probability measure under which is a Brownian motion.)
References
- 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 |