Theorems · Theorem · probability

ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le

∀ {Ω : Type u_1} {Ω' : Type u_2} {mΩ : MeasurableSpace Ω} {mΩ' : MeasurableSpace Ω'} {ν : MeasureTheory.Measure Ω'}
  {κ : ProbabilityTheory.Kernel Ω' Ω} {X : Ω → ℝ} {c : NNReal},
  ProbabilityTheory.Kernel.HasSubgaussianMGF X c κ ν →
    ∀ {ε : ℝ}, 0 ≤ ε → ∀ᵐ (ω' : Ω') ∂ν, (κ ω').real {ω | ε ≤ X ω} ≤ Real.exp (-ε ^ 2 / (2 * ↑c))

Chernoff bound on the right tail of a sub-Gaussian random variable.

Defined in

Mathlib.Probability.Moments.SubGaussian

Cited by

1 results in Mathlib

Foundations

Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound