Title

Expectations for coherent probabilities

Date of Award

2002

Availability

Article

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

First Committee Member

Subramanian Ramakrishnan, Committee Chair

Abstract

In the 1930's, Kolmogorov borrowed the axiomatic system of the Lebesgue measure as a foundation for what is now the standard theory of probability. The domain of the probability measure is assumed to possess the structure of a Boolean sigma-algebra, and the measure is assumed to be countably additive. The "expectation of a random variable" is developed as the integral of a measurable function. Around the same time as Kolmogorov's development, de Finetti introduced the notion of a "coherent" probability, consistent with the Lebesgue theory, but requiring neither countable additivity of the measure nor any sort of structure on its domain. In this thesis I present a theory of the integral, or expectation, with respect to this broader notion of a probability.

Keywords

Mathematics; Statistics

Link to Full Text

http://access.library.miami.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3056618