A Note on Conditional Exponential Moments and Onsager-Machlup Functionals
Shepp, Larry A. ; Zeitouni, Ofer
Ann. Probab., Tome 20 (1992) no. 4, p. 652-654 / Harvested from Project Euclid
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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.
Publié le : 1992-04-14
Classification:  Gaussian norms,  Onsager-Machlup,  correlation inequalities,  60G15,  60F10,  60J65 
@article{1176989796,
     author = {Shepp, Larry A. and Zeitouni, Ofer},
     title = {A Note on Conditional Exponential Moments and Onsager-Machlup Functionals},
     journal = {Ann. Probab.},
     volume = {20},
     number = {4},
     year = {1992},
     pages = { 652-654},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989796}
}

Shepp, Larry A.; Zeitouni, Ofer. A Note on Conditional Exponential Moments and Onsager-Machlup Functionals. Ann. Probab., Tome 20 (1992) no. 4, pp.  652-654. http://gdmltest.u-ga.fr/item/1176989796/