Maximal inequalities for stochastic integrals

• Autorzy: Osękowski A.
• Języki publikacji: EN

Abstrakty

EN

We find the optimal universal constant Cp (1 < p ≤ ∞) in the following inequality. If X = (Xt)t>o is a martingale and Y = [wzór] for some predictable process H taking values in [-1,1], then E[wzór].

Słowa kluczowe

EN

martingale; maximal function; martingale transform; norm inequality

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 3
• Strony: 273--287
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Osękowski A.

• Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2 02-097 Warszawa, Poland,

Bibliografia

• [Bi] K. Bichteler, Stochastic integration and Lp-theory of semimartingales, Ann. Probab. 9 (1980), 49-89.
• [B1] D. L. Burkholder, Explorations in martingale theory and its applications, in: École d’Été de Probabilités de Saint-Flour XIX - 1989, Lecture Notes in Math. 1464, Springer, Berlin, 1991, 1-66.
• [B2] D. L. Burkholder, Sharp norm comparison of martingale maximal functions and stochastic integrals, in: Proceedings of the Norbert Wiener Centenary Congress, 1994 (East Lansing, MI, 1994), Proc. Sympos. Appl. Math. 52, Amer. Math. Soc., Providence, RJ, 1997, 343-358.
• [Ol] A. Osękowski, Sharp maximal inequality for stochastic, integrals, Proc. Amer. Math. Soc. 136 (2008), 2951-2958.
• [O2] A. Osękowski, Sharp maximal inequality for martingales and stochastic integrals, Electron. Comm. Probab. 14 (2009), 17-30.
• [P] G. Peskir, The best Doob-type bounds for the maximum of Brownian paths, Progr. Probab. 43 (1998), 287-296.