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arXiv · 2311.15205

Discrete stopping times in the lattice of continuous functions

Achintya Raya Polavarapu
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Abstract

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

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Achintya Raya Polavarapu. 2023-11-26. Discrete stopping times in the lattice of continuous functions. https://arxiv.org/abs/2311.15205

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