Soft Methods for Integrated Uncertainty Modelling
Advances in Soft Computing, 2006, Volume 37/2006, 137-143, DOI: 10.1007/3-540-34777-1_18

Optional Sampling Theorem and Representation of Set-Valued Amart

Shoumei Li and Li Guan

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Abstract

In this paper, we shall prove some properties of set-valued asymptotic martingale (amart for short) and provide an optional sampling theorem. We also prove a quasi Risez decomposition theorem for set-valued amarts. Then we shall discuss the existence of selections of set-valued amarts and give a representation theorem.

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