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We study systems of differential equations driven by fast-oscillatingfunctions of a Wiener process. In the limit when the frequency of oscillationsgoes to infinity, we identify the limiting SDE systems which are driven byseveral independent Wiener processes. The solutions of the original equationsconverge to those of the limiting system in law. The limiting equations includeadditional drift terms which have the form of Stratonovich corrections. Ourresult can thus be interpreted as a reqularization of SDE systems. The systemswe study are motivated by experimental work on the motion of light-sensitiverobots and on motility-induced phase separation in bacterial colonies.

Equations driven by fast-oscillating functions of a Wiener process