Abstract:Let Q_n = B_n + J_n be the quadratic covariation matrix of a high-dimensional semimartingale, where J_n is the jump component and B_n is the diffusion component. We prove that spectral collapse occurs -- meaning the ratio of the leading eigenvalue to the trace converges to 1 and the effective rank converges to 1 -- if and only if the jump directions are geometrically aligned in a weighted sense and the background diffusion is asymptotically negligible. The proof separates into two steps: geometric alignment of jump directions forces spectral concentration of J_n; background negligibility then propagates this to the full system. We extend to the stochastic setting and prove convergence in probability under natural conditions on the jump process. The framework gives a scalar diagnostic for detecting when a high-dimensional system is dominated by extreme events.
From: Jokubas Petkevicius [view email]
[v1]
Wed, 24 Jun 2026 13:24:32 UTC (8 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。