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The Feynman-Kac Connection

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

Abstract

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
$$ ut(t,x) = \frac{1}{2}u_xx(t,x) + q(x)u(t,x)\;u(0,x) = f(x) $$
(15.1)
we can represent u(t, x) by the Feynman-Kac Formula:
$$ u(t,x) = E\left[ {f(x + {B_{t}})\exp \left( {\int_{0}^{t} {q(x + {B_{s}})ds} } \right)} \right] $$
(15.2)
.

Keywords

Brownian Motion Hedge Fund Local Martingale Unique Bounded Solution Euler Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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