Algorithmic randomness for Brownian motion

Abstract:

Algorithmic randomness is the study, under the lens of computability theory, of the question: what does it mean for an individual object to be random? Most of the theory developed so far focuses on this question in the particular case where the objects in question are infinite binary sequences. In this talk, after presenting the basics of algorithmic randomness for infinite binary sequences, we will discuss how the theory can be extended to other stochastic objects, focusing our attention on random Brownian paths, pursuing a line of research initiated in the 1978’s by Asarin and Prokovsky.

[This is joint work with Kelty Allen and Ted Slaman]