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Boundary Non-crossings of Brownian Pillow

Hashorva, Enkelejd

In: Journal of Theoretical Probability, 2010, vol. 23, no. 1, p. 193-208

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    Titre
    • Boundary Non-crossings of Brownian Pillow
    Auteur
    • Hashorva, Enkelejd. Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Theoretical Probability, 2010, vol. 23, no. 1, p. 193-208. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:320880
    Summary
    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