Notwithstanding the death of a party who made a written agreement to submit a controversy to arbitration, the arbitration proceedings may begin or continue if an application has been filed by or notice given to his personal representative. If a guardian has been appointed, the proceedings may be continued: Upon the application of the guardian; or Upon the notice to the guardian. Upon the death or incompetence of a party, the court may extend the time within which a petition to confirm, vacate, or modify the award, or to stay arbitration, must be made. If a party dies after an award was delivered, the subsequent proceedings are the same as where a party dies after a verdict.