Invariance principle, multifractional Gaussian processes and long-range   dependence
  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. 
Serge Cohen, Renaud Marty