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
Further we investigate the asymptotic behaviour of ψ(u;γ h) with γ tending to ∞ and solve a related minimisation problem.
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Hashorva, E. Boundary Non-crossings of Brownian Pillow. J Theor Probab 23, 193–208 (2010). https://doi.org/10.1007/s10959-008-0191-5
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DOI: https://doi.org/10.1007/s10959-008-0191-5
Keywords
- Boundary non-crossing probability
- Brownian pillow with trend
- Large deviations
- Smallest concave majorant
- Reproducing kernel Hilbert space
- Small ball probabilities