Functional central limit theorems for strictly stationary processes satisfying the strong mixing condition

Functional limit theorems for Lévy processes satisfying Cramér's condition

We consider a Lévy process that starts from x < 0 and conditioned on having a positive maximum. When Cramér’s condition holds, we provide two weak limit theorems as x → −∞ for the law of the (two-sided) path shifted at the first instant when it enters (0,∞), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some intere...

Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition

In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ-mixing condition.

Almost Sure Central Limit Theorem for Strictly Stationary Processes

On any aperiodic measure preserving system, there exists a square integrable function such that the associated stationary process satifies the Almost Sure Central Limit Theorem. Introduction The Almost Sure Central Limit Theorem (ASCLT), first formulated by Lévy in [9], has been studied by various authors at the end of the eighties ([6], [3], [10], [8]). This theorem gives conditions under whic...

A Central Limit Theorem and a Strong Mixing Condition.

Central Limit Theorems For Superlinear Processes

The Central Limit Theorem is studied for stationary sequences that are sums of countable collections of linear processes. Two sets of sufficient conditions are obtained. One restricts only the coefficients and is shown to be best possible among such conditions. The other involves an interplay between the coefficients and the distribution functions of the innovations and is shown to be necessary...