On Multivalued Supermartingales with Continuous Parameter: Martingale Selectors and Their Regularity

The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete parameter are studied by many authors about such questions:their convergence in several senses,the existence of martingale selections and martingale representations,etc. D.Q.Luuu20] and C.Hesss15] obtained the martingale representation theorem for multivalued martingales and proved the existence of martingale selections of mul-tivalued supermartingales by diierent methods.They used such results studying the convergence of multivalued processes.But for continuous parameter case,few authors studied such questions.Using the discrete case results,Z.P.Wang33] proved the martingale representation theorem for multivalued martingales with continuous parameter.