This paper is devoted to establish an invariance principle where the limit
process is a multifractional Gaussian process with a multifractional function
which takes its values in (1/2,1). Some properties, such as regularity and
local self-similarity of this process are studied. Moreover the limit process
is compared to the multifractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP127 the Annales de
l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques
(http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics
(http://www.imstat.org