  Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised
strong interest in recent years, motivated in particular by applications in
finance and Internet traffic modelling. Since fBm is not a semi-martingale,
stochastic integration requires specific developments. Multifractional Brownian
motion (mBm) is a Gaussian process that generalizes fBm by letting the local
H\"older exponent vary in time. This is useful in various areas, including
financial modelling and biomedicine. In this work we start from the fact,
established in \cite[Thm 2.1.(i)]{fBm_to_mBm_HerbinLebovitsVehel}, that an mBm
may be approximated, in law, by a sequence of "tangent" fBms. We used this
result to show how one can define a stochastic integral w.r.t. mBm from the
stochastic integral w.r.t. fBm, defined in \cite{Ben1}, in the White Noise
Theory sense.
