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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2019

ALMOST SURE CONVERGENCE ON CHAOSES

Résumé

We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on a fixed finite sum of chaoses forces the almost sure convergence of each chaotic component. Our strategy uses "extra random-ness" and a simple conditioning argument. These ideas are close to the spirit of Stein's method of exchangeable pairs. Some natural questions are left open in this note.
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Dates et versions

hal-01987898 , version 1 (21-01-2019)

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Guillaume Poly, Guangqu Zheng. ALMOST SURE CONVERGENCE ON CHAOSES. Proceedings of the American Mathematical Society, 2019, 147 (9), pp.4055-4065. ⟨10.1090/proc/14557⟩. ⟨hal-01987898⟩
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