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.
Consider xsuch thatα∈ {α : limβ→α τMT ,β(x) =τ MT ,α(x)}, in addition toα /∈U(x, T)
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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.