Lev davomiyligi teoremasi moduli - Lévys modulus of continuity theorem - Wikipedia

Levining davomiylik teoremasi moduli a teorema bu taxminan natija beradi deyarli aniq ning taxminiy xulq-atvori uzluksizlik moduli uchun Wiener jarayoni, bu ma'lum bo'lgan narsani modellashtirish uchun ishlatiladi Braun harakati.

Levining uzluksizlik teoremasi moduli frantsuz matematikasi nomi bilan atalgan Pol Levi.

Natija bayonoti

Ruxsat bering ${ displaystyle B: [0,1] times Omega to mathbb {R}}$ standart Wiener jarayoni bo'lishi. Keyin, deyarli aniq,

{ displaystyle lim _ {h to 0} sup _ {t, t ' leq 1; | t-t' | leq h} { frac {| B_ {t '} - B_ {t} | } { sqrt {2h log (1 / h)}}} = 1.}

Boshqacha qilib aytganda namunaviy yo'llar Braun harakatining uzluksizligi moduli mavjud

{ displaystyle omega _ {B} ( delta) = { sqrt {2 delta log (1 / delta)}}}

ehtimollik bilan va etarlicha kichik ${ displaystyle delta> 0}$ .^[1]

^ Lévy, P. Muallif profili Théorie de l'addition des variables aléatoires. 2. éd. (Frantsiya) 172-bet Zbl 0056.35903 (Monografiyalar des probabilités.) Parij: Gautier-Villars, XX, 387 p. (1954)

Pol Per Levi, Théorie de l'addition des variables aléatoires. Gautier-Villars, Parij (1937).