This is a study in patients who recently had a brain attack (stroke) and in whom no clear cause of the stroke could be identified. These strokes are likely due to a blood clot and therefore, can be called embolic stroke of undetermined source. The abbreviation is ESUS. The study will compare 2 blood thinners. Patients will be randomly assigned to either Rivaroxaban 15 mg or Aspirin 100 mg and the study is intended to show, if patients given rivaroxaban have fewer blood clots in the brain (stroke) or in other blood vessels.