F. Javier López

Asymptotic normality for the counting process of weak records and δ-records in discrete models

Let

Central limit theorems for the number of records in discrete models

\{X_n,n\ge1\}

A martingale approach to strong convergence of the number of records

be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call

Stochastic comparisons for general probabilistic cellular automata (

X_n

Stochastic comparisons and couplings for interacting particle systems

a

Records from stationary observations subject to a random trend

\delta

Central Limit Theorem for the Number of Near-Records

-record if

Local conditions for the stochastic comparison of particle systems

X_n>\max\{X_1,...,X_{n-1}\}+\delta

Limit Theorems for the Counting Process of Near-Records

, where

Asymptotic normality for the number of records from general distributions

\delta