Discrete stopping times in the lattice of continuous functions
Functional Analysis
2023-11-28 v1
Abstract
A functional calculus for an order complete vector lattice was developed by Grobler in 2014 using the Daniell integral. We show that if one represents the universal completion of as , then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in . This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in . We obtain a representation that is analogous to what is expected in probability theory.
Keywords
Cite
@article{arxiv.2311.15205,
title = {Discrete stopping times in the lattice of continuous functions},
author = {Achintya Raya Polavarapu},
journal= {arXiv preprint arXiv:2311.15205},
year = {2023}
}