Theorems · Theorem · probability

ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_increments

∀ {T : Type u_2} {Ω : Type u_3} {E : Type u_4} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {X : T → Ω → E}
  [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] [BorelSpace E] [inst_3 : NormedSpace ℝ E]
  [SecondCountableTopology E],
  ProbabilityTheory.IsGaussianProcess X P →
    ∀ {n : ℕ} {t : Fin (n + 1) → T}, ProbabilityTheory.HasGaussianLaw (fun ω i => X (t i.succ) ω - X (t i.castSucc) ω) P

The increments of a Gaussian process are Gaussian.

Defined in

Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic

Cited by

1 results in Mathlib

Foundations

Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpaceBorelSpaceNormedSpaceSecondCountableTopology