Theorems · Theorem · probability

ProbabilityTheory.Kernel.partialTraj_le

∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)} {a b : ℕ}
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))} (hba : b ≤ a),
  ProbabilityTheory.Kernel.partialTraj κ a b = ProbabilityTheory.Kernel.deterministic (Preorder.frestrictLe₂ hba) ⋯

If b ≤ a, given the trajectory up to time a, the trajectory up to time b is deterministic and is equal to the restriction of the trajectory up to time a.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Cited by

8 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound