Date of this Version
The Annals of Probability
It is proven that, for any deterministic L2[0,1] function ϕ(t),
E(exp∫10ϕ(t)dwt ∣ ∥w∥ < ε)→ 1 as ε → 0,
where wt 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.
Gaussian norms, Onsager-Machlup, correlation inequalities
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
Date Posted: 27 November 2017
This document has been peer reviewed.