Majorizing Measures and Ultrametric Spaces

• Autorzy: Bednorz W.

Identyfikatory

DOI

10.4064/ba60-1-7

• Języki publikacji: EN

Abstrakty

EN

Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.

Słowa kluczowe

EN

sample boundedness; majorizing measure; ultrametric

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 1
• Strony: 91--100
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Bednorz W.

• Institute of Mathematics Warsaw University, 02-097 Warszawa, Poland

Bibliografia

• [1] W. Bednorz, A theorem on majorizing measures, Ann. Probab. 34 (2006), 1771–1781.
• [2] -, On Talagrand’s admissible net approach to majorizing measures and boundedness of stochastic processes, Bull. Polish Acad. Sci. Math. 56 (2008), 83–91.
• [3] X. Fernique, Caractérisation de processus à trajectoires majorées ou continues, in: Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, 691–706.
• [4] N. Kôno, Sample path properties of stochastic processes, J. Math. Kyoto Univ. 20 (1980), 295–313.
• [5] J. Olejnik, On a construction of majorizing measures on subsets of Rn with special metrics, Studia Math. 197 (2010), 1–12.
• [6] G. Pisier, Conditions d’entropie assurant la continuité de certains processus et applications à l’analyse harmonique, in: Séminaire d’Analyse Fonctionnelle 1979–1980, exp. 13–14, École Polytech., Palaiseau, 1980, 43 pp.
• [7] M. Talagrand, Sample boundedness of stochastic processes under increment conditions, Ann. Probab. 18 (1990), 1–49.
• [8] -, Majorizing measures without measures, ibid. 29 (2001), 411–417.