Boundary Non-crossings of Brownian Pillow

Boundary non-crossings of Brownian pillow

Let B0(s, t) be a Brownian pillow with continuous sample paths, and let h, u : [0, 1] 2 → R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability ψ(u;h) := P{B0(s, t) + h(s, t) ≤ u(s, t), ∀s, t ∈ [0, 1]}. Further we investigate the asymptotic behaviour of ψ(u; γh) with γ tending to ∞, and solve a related minimisation problem.

Integrated vision sensor for detecting boundary crossings

State and Parameter Estimation from Boundary–Crossings

In this paper we consider the problem of estimating the state, and identifying parameters of a diffusion process, when the only available information is the crossing times of a boundary. By using a partial differential equation approach related with the computation of boundary–crossing probabilities, we derive finite dimensional reconstructors (filters) for the state and Feynman Kac type functi...

Clocking in Pillow Time without the Pillow

1512 normal enzyme. Then, they replaced the oxygen in question with a sulfur atom. The reaction didn’t work as well because, by the rules of chemistry, sulfur doesn’t like to bind to magnesium. But sulfur does like manganese and cadmium ions. So they replaced the magnesium with one of these other metal ions and measured the reaction. The researchers saw that these other metal ions restored (or ...

Border crossings: on the boundary of the physician-patient relationship.

Physicians are trained to divorce personal feelings from professional duty and to avoid those patient encounters in which we playa dual or compromised role. Yet in practice, especially in those encounters where the physician-patient relationship is our chief therapeutic tool, emotion and conflict often arise. Rather than fearing their intrusions, we should understand them to be inevitable, info...