  We consider a utility maximization problem in a broad class of markets. Apart
from traditional semimartingale markets, our class of markets includes
processes with long memory, fractional Brownian motion and related processes,
and, in general, Gaussian processes satisfying certain regularity conditions on
their covariance functions. Our choice of markets is motivated by the
well-known phenomena of the so-called "constant" and "variable depth" memory
observed in real world price processes, for which fractional and
multifractional models are the most adequate descriptions.
  We introduce the notion of a Wiener-transformable Gaussian process, and give
examples of such processes, and their representations. The representation for
the solution of the utility maximization problem in our specific setting is
presented for various utility functions.
