Feynman–Kac formula

E2031

mathematical formula result in stochastic analysis theorem in probability theory tool in mathematical physics

The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.

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Observed surface forms (1)

Surface form	Occurrences
Black–Scholes option pricing model	1

Statements (48)

Predicate	Object
instanceOf	mathematical formula ⓘ result in stochastic analysis ⓘ theorem in probability theory ⓘ tool in mathematical physics ⓘ
appliesTo	certain elliptic partial differential equations ⓘ linear parabolic partial differential equations ⓘ
assumes	existence of a corresponding diffusion process ⓘ sufficient regularity of coefficients in the PDE ⓘ
centralIn	probabilistic potential theory ⓘ stochastic control and dynamic programming ⓘ
characterizes	solutions of Schrödinger-type equations via path integrals ⓘ solutions of the heat equation via Brownian motion ⓘ
connects	partial differential equations ⓘ stochastic processes ⓘ
expresses	PDE solution as discounted expectation of terminal payoff ⓘ
field	mathematical finance ⓘ mathematical physics ⓘ partial differential equations ⓘ probability theory ⓘ stochastic processes ⓘ
generalizedBy	backward stochastic differential equations ⓘ nonlinear Feynman–Kac formulas ⓘ
historicalOrigin	work of Mark Kac on probabilistic representations of PDEs ⓘ work of Richard Feynman on path integrals ⓘ
interpretedAs	rigorous version of Feynman path integral in imaginary time ⓘ
involves	Brownian motion with drift ⓘ Markov processes ⓘ expectation with respect to a stochastic process ⓘ
namedAfter	Mark Kac ⓘ Richard Feynman ⓘ
provides	integral representation of solutions to PDEs ⓘ probabilistic representation of PDE solutions ⓘ
relatedTo	Girsanov theorem ⓘ Kolmogorov backward equation ⓘ Fokker–Planck equation ⓘ surface form: Kolmogorov forward equation
relates	Brownian motion ⓘ Schrödinger-type equations ⓘ expectations of functionals of diffusion processes ⓘ solutions of parabolic partial differential equations ⓘ
usedIn	Euclidean quantum field theory ⓘ Schrödinger equation analysis ⓘ derivatives valuation ⓘ heat equation analysis ⓘ option pricing theory ⓘ quantum mechanics ⓘ risk-neutral valuation ⓘ
uses	Itô calculus ⓘ stochastic integrals ⓘ

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Richard Feynman → knownFor → Feynman–Kac formula ⓘ

Mark Kac → notableIdea → Feynman–Kac formula ⓘ

Itô calculus → relatedConcept → Feynman–Kac formula ⓘ

Girsanov theorem → relatedTo → Feynman–Kac formula ⓘ

Brownian motion → usedIn → Feynman–Kac formula ⓘ

this entity surface form: Black–Scholes option pricing model