Before revision: We introduce a general class of multifractional stochastic processes driven by a multifractional Brownian motion  and study estimation  of their pointwise H\"older exponents (PHE) using the localized generalized quadratic variation approach.
After revision: We introduce a general class of multifractional stochastic processes driven by a multifractional Brownian motion and study estimation of their pointwise H\"older exponents (PHE) based on a new localized generalized quadratic variation approach.