We treat a convex problem to minimize mean loss function for a stochastic system operating in continuous time. The losses on time horizon $T$ arise at the jump times of a Poisson process with intensity being an unknown random process. The oracle gives the randomly noised gradients of the loss function; the noises are additive, unbiased, with the bounded dual norm in mean square sense. The goal consists in minimizing the mean integral loss over a given convex compact set in $\mathbb{R}^N$. We propose a mirror descent algorithm and prove an explicit upper bound for the mean integral loss regret. The bound is of type $C\sqrt{T}$ with an explicit constant $C$. Finally, we describe an example of optimization for a server processing a stream of incoming requests, and we discuss simulation results.