A maximal inequality for stochastic integrals

• Autorzy: Rapicki, M.
• Języki publikacji: EN

Abstrakty

EN

Assume that X is a càdlàg, real-valued martingale starting from zero, H is a predictable process with values in [−1, 1] and Y = ∫ HdX. This article contains the proofs of the following inequalities: (i) If X has continuous paths, then P(sup_{t ≥ 0} Y_t ≥ 1) ≤ 2E sup_{t ≥ 0} X_t, where the constant 2 is the best possible. (ii) If X is arbitrary, then P(sup_{t ≥ 0} Y_t ≥ 1) ≤ cE sup_{t ≥ 0} X_t; where c = 3.0446… is the unique positive number satisfying the equation 3c⁴ − 8c³ − 32 = 0. This constant is the best possible.

Słowa kluczowe

EN

martingale; sharp inequality

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 311--333
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Rapicki, M.

• Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland,

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).