Teaching: Officially, I'm retired, but in the fall of 2025, I am teaching MAT1080 Mathematical Foundation of Machine Learning.
Research: My main research interests are nonstandard analysis and probability theory. Three papers on nonstandard probability theory are Hyperfinite Lévy Processes, Nonlinear Stochastic Integrals for Hyperfinite Lévy Processes, and A Weighted Random Walk Approximation to Fractional Brownian Motion.
Textbooks: I have two textbooks in Norwegian, "Kalkulus", and "Flervariabel analyse med lineær algebra" (with Klara Hveberg), and one in English, “Spaces: An Introduction to Real Analysis”.
Book column: A column (in Norwegian) on mathematics and literature is updated when I have something to write about (which isn't very often anymore).
Tags:
Mathematics,
Stochastic analysis and finance and insurance and risk,
nonstandard analysis
Publications
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Lindstrøm, Tom Louis
(2023).
The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis.
In Hilbert, Astrid; Mastrogiacomo, Elisa; Mazzucchi, Sonia; Rüdiger, Barbara & Ugolini, Stefania (Ed.),
Quantum and Stochastic Mathematical Physics.
Springer.
ISSN 9783031140310.
p. 187–215.
doi:
10.1007/978-3-031-14031-0_9.
Full text in Research Archive
Show summary
I give a survey of Sergio Albeverio’s work in nonstandard analysis, covering applications to operator theory, stochastic analysis, Dirichlet forms, quantum mechanics, and quantum field theory, and making an attempt at putting his contributions into the historical context of what has happened in the field before and since.
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Lindstrøm, Tom Louis & Ross, David Andrew
(2023).
A nonstandard approach to asymptotic fixed point theorems.
Journal of Fixed Point Theory and Applications.
ISSN 1661-7738.
25(1).
doi:
10.1007/s11784-022-01028-6.
Full text in Research Archive
Show summary
We use methods from nonstandard analysis to unify and extend results from the theory of asymptotic fixed points on metric spaces. Among the topics we consider are Kirk’s asymptotic fixed point theorem with extensions, Boyd and Wong’s fixed point theorem, and Suzuki’s fixed point theorem for asymptotic contractions of the Meier–Keeler type. We also show how Suzuki’s asymptotic contractions of the final type can be modified to yield uniform convergence on compact and bounded sets.
View all works in NVA
Published
Nov. 30, 2010 11:20 PM
- Last modified
May 28, 2025 2:27 PM
