Strong law of large numbers for upper set-valued and fuzzy-set valued probability

Zengjing  Chen; Yuting  Lan; Gaofeng  Zong

doi:10.3934/mcrf.2015.5.435

Article Contents

2015, Volume 5, Issue 3: 435-452. Doi: 10.3934/mcrf.2015.5.435

This issue Previous Article Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process Next Article BMO martingales and positive solutions of heat equations

Strong law of large numbers for upper set-valued and fuzzy-set valued probability

1.
Qilu Securities Institute for Financial Studies, Shandong University, Jinan 250100
2.
School of Mathematics, Shandong University, Jinan 250100

Received: September 30, 2014

Revised: January 31, 2015

Published: August 2015

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Abstract

In this paper, we introduce the concepts of upper-lower set-valued probabilities and related upper-lower expectations for random variables. With a new concept of independence for random variables, we show a strong law of large numbers for upper-lower set-valued probabilities. Furthermore, we extend those concepts and theorem to the case of fuzzy-set.

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Mathematics Subject Classification: Primary: 60F15; Secondary: 52A22, 60B11.

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