Extremal behavior of hitting a cone by correlated Brownian motion with drift

Krzysztof Dȩbicki, Enkelejd Hashorva, Lanpeng Ji and Tomasz Rolski

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4171-4206

Abstract: This paper derives an exact asymptotic expression for Pxu{∃t≥0X(t)−μt∈U},asu→∞,where X(t)=(X1(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=∏i=1d[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.

Keywords: Multidimensional Brownian motion; Extremes; Exact asymptotics; First passage time; Large deviations; Quadratic programming problem; Multidimensional Pickands constants (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2018.02.002

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