The Feynman-Kac Connection

  • J. Michael Steele
Part of the Applications of Mathematics book series (SMAP, volume 45)


The basic, stripped-down, Feynman-Kac representation theorem tells us that for any pair of bounded functions q : ℝ → ℝ and f : and ℝ → ℝfor any bounded solution u(t, x) of the initial-value problem
$$ ut(t,x) = \frac{1}{2}u_xx(t,x) + q(x)u(t,x)\;u(0,x) = f(x) $$
we can represent u(t, x) by the Feynman-Kac Formula:
$$ u(t,x) = E\left[ {f(x + {B_{t}})\exp \left( {\int_{0}^{t} {q(x + {B_{s}})ds} } \right)} \right] $$


Brownian Motion Hedge Fund Local Martingale Unique Bounded Solution Euler Step 
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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • J. Michael Steele
    • 1
  1. 1.The Wharton School, Department of StatisticsUniversity of PennsylvaniaPhiladelphiaUSA

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