A Note on the Burkholder–Rosenthal Inequality

• Autorzy: Osękowski A.

Identyfikatory

DOI

10.4064/ba60-2-7

• Języki publikacji: EN

Abstrakty

EN

Let df be a Hilbert-space-valued martingale difference sequence. The paper is devoted to a new, elementary proof of the estimate... [formula].

Słowa kluczowe

EN

martingale; conditional square function

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 2
• Strony: 177--185
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Osękowski A.

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

Bibliografia

• [Bu1] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19–42.
• [Bu2] —, 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.
• [D] B. Davis, On the integrability of the martingale square function, Israel J. Math. 8 (1970), 187–190.
• [JSZ] W. B. Johnson, G. Schechtman and J. Zinn, Best constants in moment inequalities for linear combinations of independent and exchangeable random variables, Ann. Probab. 13 (1985), 234–253.
• [H1] P. Hitczenko, Best constants in martingale version of Rosenthal’s inequality, ibid. 18 (1990), 1656–1668.
• [H2] —, On a domination of sums of random variables by sums of conditionally independent ones, ibid. 22 (1994), 453–468.
• [KS] S. Kwapien and J. Szulga, Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, ibid. 19 (1991), 369–379.
• [N] S. V. Nagaev, On probability and moment inequalities for supermartingales and martingales, Acta Appl. Math. 79 (2003), 35–46.
• [O] A. Osekowski, Sharp Martingale and Semimartingale Inequalities, Monograf. Mat. 72, Birkhäuser, Basel, 2012.
• [P] I. Pinelis, Optimum bounds for the distributions of martingales in Banach spaces, Ann. Probab. 22 (1994), 1679–1706.
• [R] H. P. Rosenthal, On the subspaces of Lp (p > 2) spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273–303.
• [T] M. Talagrand, Isoperimetry and integrability of the sum of independent Banachspace valued random variables, Ann. Probab. 17 (1989), 1546–1570.