Theorems · Theorem · probability

ProbabilityTheory.IsGaussianProcess.shift

∀ {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] [inst_5 : Add T],
  ProbabilityTheory.IsGaussianProcess X P →
    ∀ (t₀ : T), ProbabilityTheory.IsGaussianProcess (fun t ω => X (t₀ + t) ω - X t₀ ω) P

Defined in

Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic

Cited by

1 results in Mathlib

Foundations

Depth 309 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpaceBorelSpaceNormedSpaceSecondCountableTopologyAdd