Theorems · Theorem · probability

MeasureTheory.stoppedValue_lowerCrossingTime

∀ {Ω : Type u_1} {a b : ℝ} {f : ℕ → Ω → ℝ} {N n : ℕ} {ω : Ω},
  MeasureTheory.lowerCrossingTime a b f N n ω ≠ N →
    MeasureTheory.stoppedValue f (fun ω => ↑(MeasureTheory.lowerCrossingTime a b f N n ω)) ω ≤ a

Defined in

Mathlib.Probability.Martingale.Upcrossing

Cited by

4 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound