Investigating the Relationship between Limit Theorems in Probability Theory and Ergodic Theory

Please enable javascript in your browser.

Movahhedrad, Ali | 2022

205 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55177 (02)
University: Sharif University of Technolog
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra
Abstract:
Birkhoff's ergodic theorem in dynamical systems and ergodic theory, and the strong law of large numbers in probability theory are among the fundamental theorems of the two fields, which are closely related. Thus Birkhoff's ergodic theorem directly yields the strong law of large numbers. Attempts were then made to express some limit theorems in probability theory in the form of dynamic systems, such as the central limit theorem, which was expressed in the form of dynamic systems, and even generalizations of It was also obtained. In this paper, we will investigate the above and similar connections between probability limit theorems and well-known theorems in ergodic theory
Keywords:
Dynamical Systems ; Central Limit Theorem ; Ergodic Theory ; Large Numbers Strong Law ; Birkhoff's Ergodic Theorem

No TOC