Debicki, K, Hashorva, E, Ji, L et al. (1 more author) (2018) Extremal behaviour of hitting a cone by correlated Brownian motion with drift. Stochastic Processes and their Applications, 128 (12). pp. 4171-4206. ISSN 0304-4149
Abstract
This paper derives an exact asymptotic expression for
Pxu {∃t≥0X(t) − μt ∈ U}, as u → ∞,
where X(t) = (X₁1(t), . . . , Xd (t))⊤, t ≥ 0 is a correlated d-dimensional Brownian motion starting at the point xu = −αu with α ∈ Rd , μ ∈ Rd and U = Πd i=1[0,∞). The derived asymptotics depends on the solution of an underlying multidimensional quadratic optimization problem with constraints, which leads in some cases to dimension-reduction of the considered problem. Complementary, we study asymptotic distribution of the conditional first passage time to U, which depends on the dimension reduction phenomena.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier B.V. This is an author produced version of a paper published in Stochastic Processes and their Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Multidimensional Brownian motion; Extremes; Exact asymptotis; First passage time; Large deviations; Quadratic programming problem; Multidimensional Pickands constants |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Feb 2018 14:11 |
Last Modified: | 16 Feb 2019 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.spa.2018.02.002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127327 |