Abstract
A stationary Poisson sequence (X n) nϵ Z can be represented as X n = M( τ n A), where A is a set in a measure space (E, E, μ), τ is an invertible measure-preserving transformation on ( E, E , μ), and M is a random Poisson measure on (E, E, μ) . We explore the relationship between the ergodic properties of the sequence and the properties of τ, and construct examples with various ergodic properties using a stacking method on the half-line [0, ∞). We also investigate the spectral properties of the sequence.
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