Regularity of multifractional moving average processes with random Hurst exponent

A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer as It\^o-mBm. It shown that It\^o-mBm locally self-similar. In contrast mBm, its pathwise regularity almost unaffected by the roughness of functional parameter. The properties are established via a new polynomial moment condition similar Kolmogorov-Chentsov theorem, allowing for local H\"older exponents. Our results applicable broad class moving average processes where and long memory may be decoupled, e.g. generalization Mat\'ern process.