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In other words this user will perform any changes in Jira required by the definition of the repeating. This user can be (but not must be) the reporter or the assignee of newly created issue. Reporter and assignee can be set in proper fields in the form when setup the repeating.
Owner For single definition the owner of the repeating may be changed by any user who will edit the definition of the repeating or for multiple issues by administrators by editing this definition at issue view (editor will be new owner). Administrators can change the owner for multiple definitions using bulk operations- see How to change owner of the definition of the repeating?