Theorems · Theorem · probability

MeasureTheory.IsPredictable.martingalePart_eq

∀ {Ω : Type u_1} {E : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] {f : ℕ → Ω → E} {ℱ : MeasureTheory.Filtration ℕ m0}
  [MeasureTheory.SigmaFiniteFiltration μ ℱ],
  MeasureTheory.IsStronglyPredictable ℱ f →
    (∀ (n : ℕ), MeasureTheory.Integrable (f n) μ) → ∀ (n : ℕ), MeasureTheory.martingalePart f ℱ μ n =ᵐ[μ] f 0

Defined in

Mathlib.Probability.Martingale.Centering

Cited by

0 results in Mathlib

Foundations

Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFiniteFiltration