The Law of the Iterated Logarithm for Algorithmically Random Brownian Motion 1st Edition by Bjorn Kjos Hanssen, Anil Nerode ISBN 9783540727347

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ISBN 10: 
ISBN 13: 9783540727347
Author: Bjorn Kjos Hanssen, Anil Nerode

Algorithmic randomness is most often studied in the setting of the fair-coin measure on the Cantor space, or equivalently Lebesgue measure on the unit interval. It has also been considered for the Wiener measure on the space of continuous functions. Answering a question of Fouché, we show that Khintchine’s law of the iterated logarithm holds at almost all points for each Martin-Löf random path of Brownian motion. In the terminology of Fouché, these are the complex oscillations. The main new idea of the proof is to take advantage of the Wiener-Carathéodory measure algebra isomorphism theorem.

The Law of the Iterated Logarithm for Algorithmically Random Brownian Motion 1st Table of contents:

• Algorithmically Random Brownian Motion
• The Law of the Iterated Logarithm: Basics
• Results for Algorithmically Random Processes
• Proof Techniques and Methodology
• Applications in Probability Theory
• Connections to Other Stochastic Processes
• Challenges and Open Problems
• Future Research Directions

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