2023/12/03 by Jin, Xiong
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2312.01390
We prove a Chung-Fuchs type theorem for skew product dynamical systems such that for a measurable function on such a system, if its Birkhoff average converges to zero almost surely, and on typical fibres its Birkhoff sums have a non-trivial independent structure, then its associated generalised random walk oscillates, that is the supremum of the random walk equals to +∞ and the infimum equals to -∞.