2022/07/19 by Sovanlal Mondal, Mondal, Sovanlal
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2207.09032
In this paper, we will introduce the `grid method' to prove that the extreme case of oscillation occurs for the averages obtained by sampling a flow along the sequence of times of the form \nα: n∈ ℕ\, where α is a positive non-integer rational number. Such behavior of a sequence is known as the `strong sweeping out property'. By using the same method, we will give an example of a general class of sequences which satisfy the `strong sweeping out' property. This class of sequences may be useful to solve the longstanding open problem: for a given irrational α, whether the sequence (nα) is `pointwise bad' for Lp or not. In the process of proving these results, we will prove a continuous version of the Conze principle.