  We propose an inertial forward-backward splitting algorithm to compute the
zero of a sum of two monotone operators allowing for stochastic errors in the
computation of the operators. More precisely, we establish almost sure
convergence in real Hilbert spaces of the sequence of iterates to an optimal
solution. Then, based on this analysis, we introduce two new classes of
stochastic inertial primal-dual splitting methods for solving structured
systems of composite monotone inclusions and prove their convergence. Our
results extend to the stochastic and inertial setting various types of
structured monotone inclusion problems and corresponding algorithmic solutions.
Application to minimization problems is discussed.
