Theorems · Theorem · probability

MeasureTheory.crossing_pos_eq

∀ {Ω : Type u_1} {a b : ℝ} {f : ℕ → Ω → ℝ} {N n : ℕ},
  a < b →
    MeasureTheory.upperCrossingTime 0 (b - a) (fun n ω => (f n ω - a)⁺) N n =
        MeasureTheory.upperCrossingTime a b f N n ∧
      MeasureTheory.lowerCrossingTime 0 (b - a) (fun n ω => (f n ω - a)⁺) N n =
        MeasureTheory.lowerCrossingTime a b f N n

Defined in

Mathlib.Probability.Martingale.Upcrossing

Cited by

1 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound