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Home > Feynman-Kac formula

Suppose we are given the PDE

subject to the terminal condition

where μ, σ², ψ are known functions and u is the unknown. Then FK tells us that the solution can be written as an expectation:

where X is an Itô process driven by the equation

This expectation can then be approximated using Monte Carlo or quasi-Monte Carlo methods

See also

• Itô's lemma

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Topics: Feynman-Kac Formula Expectation Process Pdes Carlo Stochastic...

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Feynman diagramA Feynman diagram is a bookkeeping device for performing calculations in quantum field theory, invented by American physicist Richard Feynman. The problem of calculating scattering cross sections in particle physics reduces to summing over the amplitudes Feynman pointThe Feynman point comprises the 762nd through 767th decimal places of Pi, consisting of the digit 9 repeated six times. Since is an irrational number with an infinite non-repeating decimal expansion which may well be normal, any given sequence of any leng Feynman-Kac formulaThe Feynman-Kac formula establishes a link between partial differential equations (PDEs) and stochastic processes. It offers yet another method of solving certain PDEs: by simulating random paths of a stochastic process. Suppose we are given the PDE : sub