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Summary of paper: The paper studies a class of asynchronous methods to solving optimization problems in which the objective function is an integral functional of a random process or variable integrated against a probability measure. The class of problem assumed is that the argument of the functional for each non-zero measure set or outcome in the sample space upon which the measure is defined will produce a convex function. In this case the authors demonstrate that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. The authors are able to then propose based on these results specialised asynchronous procedures based on multi-core parallelization schemes for stochastic gradient based optimization algorithms which behave analogously to synchronous procedures. Quality: The problem statement and all assumptions are very carefully set out and clearly written and explained with regard to the meaning and significance of such assumptions.