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arXiv · 0809.4560

Boundary non-crossings of Brownian pillow

Enkelejd Hashorva
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Abstract

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 ψ(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 $ψ(u;γh)$ with $γ$ tending to infinity, and solve a related minimisation problem.

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Enkelejd Hashorva. 2008-09-26. Boundary non-crossings of Brownian pillow. https://doi.org/10.1007/s10959-008-0191-5

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