here - Joint Mathematics Meetings

The original (non-specific) Rice formula: The proof◮ So far, everything is deterministicU u (f , T ) = lim |ḟ (t)| δ ε (f (t) − u) 1 (0,∞) (f (t)) dtε→0∫T◮ Take expectations, with some sleight of hand{ ∫E{U u (f , T )} = E limε→0 T∫===∫T{lim Eε→0lim∫ ∞T ε→0 x=−∞∫ ∞∫T0}|ḟ (t)| δ ε(f (t) − u) 1 (0,∞) (f (t)) dt}|ḟ (t)| δ ε (f (t) − u) 1 (0,∞) (f (t)) dt∫ ∞y=0|y| p t (u, y) dydt|y| δ ε (x − u) p t (x, y) dxdy dt