  Stochastic non-local conservation law equation in the presence of
discontinuous flux functions is considered in an $L^{1}\cap L^{2}$ setting. The
flux function is assumed bounded and integrable (spatial variable). Our result
is to prove existence and uniqueness of weak solutions. The solution is strong
solution in the probabilistic sense. The proofs are constructive and based on
the method of characteristics (in the presence of noise), It\^o-Wentzell-Kunita
formula and commutators. Our results are new , to the best of our knowledge,
and are the first nonlinear extension of the seminar paper [20] where the
linear case was addressed.
