Theorems · Definition · probability

ProbabilityTheory.Kernel.trajMeasure

{X : ℕ → Type u_1} →
  [inst : (n : ℕ) → MeasurableSpace (X n)] →
    MeasureTheory.Measure (X 0) →
      (κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))) →
        [∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] → MeasureTheory.Measure ((n : ℕ) → X n)

Distribution of the trajectory obtained by starting with μ₀ and iterating the kernels κ.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.Traj

Cited by

2 results in Mathlib

Foundations

Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceProbabilityTheory.IsMarkovKernel