  Stochastic parareal (SParareal) is a probabilistic variant of the popular
parallel-in-time algorithm known as parareal. Similarly to parareal, it
combines fine- and coarse-grained solutions to an ordinary differential
equation (ODE) using a predictor-corrector (PC) scheme. The key difference is
that carefully chosen random perturbations are added to the PC to try to
accelerate the location of a stochastic solution to the ODE. In this paper, we
derive superlinear and linear mean-square error bounds for SParareal applied to
nonlinear systems of ODEs using different types of perturbations. We illustrate
these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE,
showing a good match between theory and numerics.
