Regularity and identification of generalized multifractional Gaussian processes

In this article a class of multifractional processes is introduced, called Generalized Multifractional Gaussian Process (GMGP). For such multifractional models, the Hurst exponent of the celebrated Fractional Brownian Motion is replaced by a function, called the multifractional function, which may be irregular. The main aim of this paper is to show how to identify irregular multifractional functions in the setting of GMGP. Examples of discontinuous multifractional functions are also given.