A Note on Conditional Exponential Moments and Onsager-Machlup Functionals
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Statistics Papers
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Gaussian norms
Onsager-Machlup
correlation inequalities
Probability
Onsager-Machlup
correlation inequalities
Probability
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Shepp, Larry A
Zeitouni, Ofer
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Abstract
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.
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1992
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The Annals of Probability