Sharp norm inequalities for martingales and their differential subordinates

• Autorzy: Osękowski, A.
• Języki publikacji: EN

Abstrakty

EN

Suppose ƒ = (ƒn), g = (gn) are martingales with respect to the same filtration, satisfying |ƒn-ƒn-i| ≤ |gn -gn-1|, n = 1,2,..., with probability 1. Under some assumptions on ƒo, go and an additional condition that one of the processes is nonnegative, some sharp inequalities between the pth norms of ƒ and g, 0 < p < ∞, are established. As an application, related sharp inequalities for stochastic integrals and harmonic functions are obtained.

Słowa kluczowe

PL

martyngał; całka stochastyczna; funkcja harmoniczna

EN

martingale; differential subordination; stochastic integral; harmonic function; norm inequality

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 4
• Strony: 373-385
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Osękowski, A.

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

Bibliografia

• [1] D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647-702.
• [2] —, Explorations in martingale theory and its applications, Ecole d'Ete de Probabilites de Saint-Flour XIX—1989, Lecture Notes in Math. 1464, Springer, Berlin, 1991, 1-66.
• [3] —, Strong differential subordination and stochastic integration, Ann. Probab. 22 (1994), 995-1025.
• [4] —, Some extremal problems in martingale theory and harmonic analysis, in: Harmonic Analysis and Partial Differential Equations (Chicago, IL, 1996), Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 1999, 99-115.
• [5] A. Osękowski, Inequalities for dominated martingales, Bernoulli 13 (2007), 54-79.