Displaying similar documents to “On a model for the storage of files on a hardware: statistics at a fixed time and asymptotic regimes.”

Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

Similarity:

A Large Deviation Principle (LDP) is proved for the family 1 n ∑ 1 n 𝐟 ( x i n ) · Z i n where the deterministic probability measure 1 n ∑ 1 n δ x i n converges weakly to a probability measure R and ( Z i n ) i ∈ ℕ are ℝ d -valued independent random variables whose distribution depends on x i n and satisfies the following exponential moments condition: sup i , n 𝔼 e α * | Z i n | < + ∞ forsome 0 < α * < + ∞ . In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Convex rearrangements of Lévy processes

Youri Davydov, Emmanuel Thilly (2007)

ESAIM: Probability and Statistics

Similarity:

In this paper we study asymptotic behavior of convex rearrangements of Lévy processes. In particular we obtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measure is regularly varying at with exponent ∈ (1,2).