Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F1...