Boundary non-crossings of Brownian pillow

Details Boundary non-crossings of Brownian pillow Boundary non-crossings of Brownian pillow

2008-09-26

arxiv.org/abs/0809.4560v1

Mathematics

Probability

14 pages

Scientific paper

Let B_0(s,t) be a Brownian pillow with continuous sample paths, and let h,u:[0,1]^2\to R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability \psi(u;h):=P{B_0(s,t)+h(s,t) \le u(s,t), \forall s,t\in [0,1]}. Further we investigate the asymptotic behaviour of $\psi(u;\gamma h)$ with $\gamma$ tending to infinity, and solve a related minimisation problem.

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