Exponential Decay of Lifetimes and a Theorem of Kac on Total Occupation Times

Masayoshi Takeda

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Let (1/2D, H1(Rd)) be the Dirichlet integral and (Bt, Pcursive Greek chiW) the Brownian motion on Rd. Let μ be a finite positive measure in the Kato class and Aμt the additive functional associated with μ. We prove that for a regular domain D of Rd limβ→∞ 1/β log Pcursive Greek chiW (AμτD > β) = - inf {1/2D(u, u) : u ∈ C0(D), ∫D u2 dμ = 1} for any cursive Greek chi ∈ D, where τD is the exit time from D. As an application, we consider the integrability of Wiener functional exp (AμτD).

Original languageEnglish
Pages (from-to)235-247
Number of pages13
JournalPotential Analysis
Volume11
Issue number3
DOIs
Publication statusPublished - 1999 Jan 1

Keywords

  • Additive functional
  • Dirichlet form
  • Exponenial decay of lifetime
  • Large deviation
  • Time change

ASJC Scopus subject areas

  • Analysis

Fingerprint

Dive into the research topics of 'Exponential Decay of Lifetimes and a Theorem of Kac on Total Occupation Times'. Together they form a unique fingerprint.

Cite this