  We establish the stochastic Strichartz estimate for the fractional
Schr\"odinger equation with multiplicative noise. With the help of the
deterministic Strichartz estimates, we prove the existence and uniqueness of a
global solution to the stochastic fractional nonlinear Schr\"odinger equation
in $L^2(\mathbb{R}^n)$. In addition, we also prove a general blow up result by
deriving a localized virial estimate and the generalized Strauss inequality
with a restricted class of initial data.
