On Talagrand's admissible net approach to majorizing measures and boundedness of stochastic processes

• Autorzy: Bednorz W.
• Języki publikacji: EN

Abstrakty

EN

We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded increments.

Słowa kluczowe

EN

majorizing measure; sample boundedness

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 1
• Strony: 83--91
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Bednorz W.

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

Bibliografia

• [1] W. Bednorz, A theorem on majorizing measures, Ann. Probab. 34 (2006), 1771-1781.
• [2] X. Fernique, Régularité des trajectoires des fonctions aléatoires gaussiennes, in: École d’Été de Probabilités de Saint-Flour, IV-1974, Lecture Notes in Math. 480, Springer, Berlin, 1975, 1-96.
• [3] M. Talagrand, Sample boundedness of stochastic processes under increment conditions, Ann. Probab. 18 (1990), 1-49.
• [4] -, Majorizing measures without measures, ibid. 29 (2001), 411-417.
• [5] -, The Generic Chaining. Upper and Lower Bounds of Stochastic Processes, Springer, Berlin, 2005.