Open Access
April, 1992 A Note on Conditional Exponential Moments and Onsager-Machlup Functionals
Larry A. Shepp, Ofer Zeitouni
Ann. Probab. 20(2): 652-654 (April, 1992). DOI: 10.1214/aop/1176989796


It is proven that, for any deterministic $L^2\lbrack 0,1\rbrack$ function $\phi(t)$, $E\bigg(\exp\int^1_0\phi(t)dw_t\bigg\arrowvert \|w\| < \varepsilon\bigg) \rightarrow 1\,\text{as}\,\varepsilon \rightarrow 0,$ where $w_t$ is a standard Brownian motion and $\|\cdot\|$ is any "reasonable" norm on $C_0\lbrack 0,1\rbrack$. Applications to the computation of Onsager-Machlup functionals are pointed out.


Download Citation

Larry A. Shepp. Ofer Zeitouni. "A Note on Conditional Exponential Moments and Onsager-Machlup Functionals." Ann. Probab. 20 (2) 652 - 654, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0756.60038
MathSciNet: MR1159564
Digital Object Identifier: 10.1214/aop/1176989796

Primary: 60G15
Secondary: 60F10 , 60J65

Keywords: Correlation inequalities , Gaussian norms , Onsager-Machlup

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
Back to Top