Boundary Non-crossings of Brownian Pillow

Enkelejd Hashorva ()
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Enkelejd Hashorva: University of Bern

Journal of Theoretical Probability, 2010, vol. 23, issue 1, 193-208

Abstract: Abstract Let B 0(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 $$\psi(u;h):=\mathbf{P}\big\{B_{0}(s,t)+h(s,t)\leq u(s,t),\forall s,t\in[0,1]\big\}.$$ Further we investigate the asymptotic behaviour of ψ(u;γ h) with γ tending to ∞ and solve a related minimisation problem.

Keywords: Boundary non-crossing probability; Brownian pillow with trend; Large deviations; Smallest concave majorant; Reproducing kernel Hilbert space; Small ball probabilities; 60J65; 60F10; 60G15; 60G70 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-008-0191-5

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