A Note on Conditional Exponential Moments and Onsager-Machlup Functionals
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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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