The generalized multifractional field: A nice tool for the study of the generalized multifractional Brownian motion (Q1565956)

The fractional Brownian motion sheet is extended to a Gaussian field \(Y\) defined either with respect to its covariance kernel or as a Wiener integral. Then, a Gaussian process (namely a generalized multifractional Brownian motion, GMB motion) \(X\) is defined as \(X: t\mapsto Y(t,t)\); the Hölder exponent of such a process may differ widely point to point. A wavelet decomposition of \(Y\) allows to obtain some uniform Hölder properties. Finally, the difference between two GMB motions which have the same local Hölder exponents is a smoother process (i.e. its Hölder exponent is larger).