The aim of this paper is to establish Strassen’s law of the iterated logarithm for negatively associated random vectors under the /nite second moment. c © 2001 Elsevier Science B.V. All rights reserved. MSC: Primary 60F15; 60F17

In this paper we establish limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random sequences.

We implement the Azencott method to prove moderate deviation principle for two-dimensional incompressible stochastic Navier–Stokes equations in a bounded domain. The Strassen’s compact law of iterated logarithm is then achieved as an application.

Let fXn;n 1g be i.i.d. R d-valued random variables. We prove Partial Moderate Deviation Principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.

In this paper we establish path properties and a generalized uniform law of the iterated logarithm (LIL) for strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random fields taking values in l∞-space.

Exact rates of convergence which are of the law of the iterated logarithm type are investigated for recursive stochastic diierence equations in Ba-nach spaces. The results are applied to autoregressive processes and to an averaging method.

We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.

In this note, we obtain a Chung's integral test for self-normalized sums of i.i.d. random variables. Furthermore, we obtain a convergence rate of Chung law of the iterated logarithm for self-normalized sums.

We show a Marcinkiewicz–Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in L r ( ∈ 0 , 2 ) and almost surely. Then, we obtain iterated logarithm such arrays under weaker moment condition than the existing one.