Introduces hyperplane α-quantile for R^d cadlag processes, proves its continuity in Skorokhod J1 topology, and establishes weak convergence of the quantile and its first hitting time when the limit process is multidimensional Brownian motion.
(1999).L´ evy processes and infinitely divisible distributions
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Note on the Weak Convergence of Hyperplane $\alpha$-Quantile Functionals and Their Continuity in the Skorokhod J1 Topology
Introduces hyperplane α-quantile for R^d cadlag processes, proves its continuity in Skorokhod J1 topology, and establishes weak convergence of the quantile and its first hitting time when the limit process is multidimensional Brownian motion.