Abstract
In this paper we investigate the properties of a remarkable class of Gaussian sequences arising from E.M. Stein’s probabilistic approach to continuity principle in ergodic theory followed by spectacular applications in real analysis due to J. Bourgain and further investigations of the second named author. For such sequences, we obtain a nearly complete picture of the properties of the oscillations and describe the weak and strong convergence properties of associated sojourn times.
Supported by International Science Foundation and Russian Foundation for Basic Research
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Lifshits, M., Weber, M. (1998). Oscillations of Gaussian Stein’s Elements. In: Eberlein, E., Hahn, M., Talagrand, M. (eds) High Dimensional Probability. Progress in Probability, vol 43. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8829-5_15
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DOI: https://doi.org/10.1007/978-3-0348-8829-5_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9790-7
Online ISBN: 978-3-0348-8829-5
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