Stochastic Processes, Dynamical Systems, and Extreme Value Laws

Wallé, Jermain (2025) Stochastic Processes, Dynamical Systems, and Extreme Value Laws. Master's Thesis / Essay, Mathematics.

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Abstract

In the study of discrete dynamical systems the orbit of a starting point is observed under repeated iterations of a specified function. Complex and chaotic behavior can arise from simple maps, prohibiting quantitative analysis in favor of a more qualitative approach to studying the asymptotics of the system. Replacing the initial condition with a random variable results in a probabilistic process for which extreme value laws can be determined, i.e. the distribution of the maximum of the resulting sequence of random variables. In this thesis, the Renyi map is used as a case study for exploring extreme value laws. By varying the parameter in the map, different behavior is observed. Boer and Sterk have derived an extreme value law for the case when beta is a positive integer, using generalized Fibonacci numbers. Following this up, we shed light on the work done by Leadbetter on extreme value distributions to put it into context with the Renyi map, giving handholds on how to derive extreme value laws for different parameter values.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Sterk, A.E.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	10 Apr 2025 07:37
Last Modified:	10 Apr 2025 07:37
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/35052

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