Version 1
: Received: 30 August 2024 / Approved: 30 August 2024 / Online: 2 September 2024 (12:06:03 CEST)
How to cite:
Imomov, A. A.; Tukhtaev, E. E.; Sztrik, J. On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications. Preprints2024, 2024082250. https://doi.org/10.20944/preprints202408.2250.v1
Imomov, A. A.; Tukhtaev, E. E.; Sztrik, J. On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications. Preprints 2024, 2024082250. https://doi.org/10.20944/preprints202408.2250.v1
Imomov, A. A.; Tukhtaev, E. E.; Sztrik, J. On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications. Preprints2024, 2024082250. https://doi.org/10.20944/preprints202408.2250.v1
APA Style
Imomov, A. A., Tukhtaev, E. E., & Sztrik, J. (2024). On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications. Preprints. https://doi.org/10.20944/preprints202408.2250.v1
Chicago/Turabian Style
Imomov, A. A., Erkin E. Tukhtaev and János Sztrik. 2024 "On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications" Preprints. https://doi.org/10.20944/preprints202408.2250.v1
Abstract
In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with remainder depending on the types of remainder. We also prove several important theorems on the asymptotic representation of integrals of Karamata functions. Under certain conditions, we observe a “narrowing” of classes of slowly varying functions concerning the types of remainder. At the end of the paper, we discuss the possibilities of application of slowly varying functions in the theory of stochastic branching systems. In particular, under the condition of the finiteness of the moment of the type Exlnx for the particle transformation intensity, it is established that the property of slow variation with remainder is implicitly present in the asymptotic structure of a non-critical Markov branching random system.
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
