English

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 E\mathcal{E} was developed by Grobler in 2014 using the Daniell integral. We show that if one represents the universal completion of E\mathcal{E} as C(K)C^\infty(K), then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in C(K)C^\infty(K). This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in C(K)C^\infty(K). 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}
}