ScholarlyCommons

Title

A Note on Conditional Exponential Moments and Onsager-Machlup Functionals

Author(s)

Larry A. Shepp, University of Pennsylvania
Ofer Zeitouni

Document Type

Journal Article

Date of this Version

1992

Publication Source

The Annals of Probability

Volume

20

Issue

2

Start Page

652

Last Page

654

DOI

10.1214/aop/1176989796

Abstract

It is proven that, for any deterministic L²[0,1] function ϕ(t),

E(exp∫¹₀ϕ(t)dw_t ∣ ∥w∥ < ε)→ 1 as ε → 0,

where w_t is a standard Brownian motion and ∥⋅∥ is any "reasonable" norm on C₀[0,1]. Applications to the computation of Onsager-Machlup functionals are pointed out.

Keywords

Gaussian norms, Onsager-Machlup, correlation inequalities

Recommended Citation

Shepp, L. A., & Zeitouni, O. (1992). A Note on Conditional Exponential Moments and Onsager-Machlup Functionals. The Annals of Probability, 20 (2), 652-654. http://dx.doi.org/10.1214/aop/1176989796