  Multifractional Brownian motion is an extension of the well-known fractional
Brownian motion where the Holder regularity is allowed to vary along the paths.
In this paper, two kind of multi-parameter extensions of mBm are studied: one
is isotropic while the other is not. For each of these processes, a moving
average representation, a harmonizable representation, and the covariance
structure are given. The Holder regularity is then studied. In particular, the
case of an irregular exponent function H is investigated. In this situation,
the almost sure pointwise and local Holder exponents of the multi-parameter mBm
are proved to be equal to the correspondent exponents of H. Eventually, a local
asymptotic self-similarity property is proved. The limit process can be another
process than fBm.
