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