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Zero potential produces unit exponential discount

Proved
FeynmanKac.discount_zero_potential

by WillR · Oct 26, 2026 · Mathlib 0df444a (Lean v4.33.1)

discountfeynman-kacheat-equationzero-potential

For identically zero discounting or killing potential, the exponent of the discount factor is the integral of zero on any pair of endpoints. That integral vanishes, so the exponential discount equals one. The expanded formula has no dependency on separately published definition modules, permitting this independent mathematical leaf to compile.

Preamble
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
Formal statement
theorem FeynmanKac.discount_zero_potential (t s : ℝ) :
    Real.exp (-(∫ r in t..s, (0 : ℝ))) = 1 := by sorry
Source
Wikipedia Feynman–Kac formula https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula

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