  Stochastic integration with respect to Gaussian processes, such as fractional
Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised
strong interest in recent years, motivated in particular by applications in
finance, Internet traffic modeling and biomedicine. The aim of this work to
define and develop, using White Noise Theory, an anticipative stochastic
calculus with respect to a large class of Gaussian processes, denoted G, that
contains, among many other processes, Volterra processes (and thus fBm) and
also mBm. This stochastic calculus includes a definition of a stochastic
integral, It\^o formulas (both for tempered distributions and for functions
with sub-exponential growth), a Tanaka Formula as well as a definition, and a
short study, of (both weighted and non weighted) local times of elements of G .
In that view, a white noise derivative of any Gaussian process G of G is
defined and used to integrate, with respect to G, a large class of stochastic
processes, using Wick products. A comparison of our integral wrt elements of G
to the ones provided by Malliavin calculus in [AMN01] and by It\^o stochastic
calculus is also made. Moreover, one shows that the stochastic calculus with
respect to Gaussian processes provided in this work generalizes the stochastic
calculus originally proposed for fBm in [EVdH03, BS{\O}W04, Ben03a] and for mBm
in [LLV14, Leb13, LLVH14]. Likewise, it generalizes results given in [NT06] and
some results given in [AMN01]. In addition, it offers alternative conditions to
the ones required in [AMN01] when one deals with stochastic calculus with
respect to Gaussian processes.
