6 1. INTRODUCTION
is a centered Gaussian process and all the information about the sample paths is
contained in the covariance function. From the results of Chapter 4, we already
have upper bounds on
of increments of the solution. We complete the
analysis by obtaining sharp lower bounds for these increments; this requires precise
estimates of integrals related to (1.4).
The last part of the article, Chapter 6, gathers the somewhat technical but
crucial sharp estimates on integrals of increments of a class of generalized Riesz
potentials that also involve the smoothed version of the fundamental solution of
the wave equation.