A representation theorem for set-valued submartingales. (English) Zbl 07880484
Summary: The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales.
Keywords:
set-valued integrals; set-valued martingales; random sets; set-valued stochastic processes; interval-valued martingale; martingale representation theoremReferences:
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