Mathematics Research Seminar Series: Two Ways of Defining Conditional Expectation in Uncertainty Space

Mathematics Research Seminar Series
Two Ways of Defining Conditional Expectation in Uncertainty Space

by Michael Frondoza, MSU-IIT

Date: Wednesday, 19 October 2022
Time: 4:30 pm
Venue: https://bit.ly/AdmuMathSeminar

Uncertain measures and uncertain variables were defined by Baoding Liu in 2007. Choquet integral with respect to an uncertain measure and some of its properties are discussed.

First, we define conditional expectations with respect to algebras in an uncertainty space. In this setting, a version of the Radon-Nikodym Theorem for uncertain measures is used to show the existence of conditional expectations of non-negative uncertain variables. The definition is then extended to uncertain variables of arbitrary sign. Properties of conditional expectations based on this definition are presented.

Finally, we provide another way of defining a conditional expectation of an uncertain variable with respect to an algebra which minimizes the integral of a certain quadratic expression. We justify the existence of conditional expectations and prove some of their properties.