Capacity estimates, boundary crossings and the ornstein-uhlenbeck process in wiener space

Endre Csáki, Davar Khoshnevisan, Zhan Shi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let T1 denote the first passage time to 1 of a standard Brownian motion. It is well known that as λ → ∞, P(T1 > λ)∼ cλ−1/2, where c = (2/π)1/2. The goal of this note is to establish a capacitarian version of this result. Namely, we will prove the existence of positive and finite constants K1 and K2 such that for all λ > ee, (formula presented) where ‘log’ denotes the natural logarithm, and Cap is capacity on Wiener space.

Original languageEnglish
Pages (from-to)103-109
Number of pages7
JournalElectronic Communications in Probability
Volume4
DOIs
Publication statusPublished - Jan 1 1999

Keywords

  • Brownian sheet
  • Capacity on Wiener space
  • Ornstein-Uhlenbeck process
  • Quasi-sure analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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