Remarks and corrections on "An existence theorem for stochastic functional differential equations with delays under weak assumptions, Statistics and Probability Letters 78, 2008" by N. Halidias and Y. Ren

In this note we would like to give some remarks and open problems concerning comparison results for stochastic functional differential equations. Our starting point was the paper by [N. Halidias, Y. Ren, 2008. An existence theorem for stochastic functional differential equations with delays under weak assumptions, Statistics and Probability Letters, 78] where one can find some incorrect arguments in the comparison result. However, as we shall prove in this note, the results in that paper are true under some more restrictive conditions on the data.