Multiradial Regular Variation

Source abstract

We introduce and study multiradial regular variation of random fields, allowing componentwise thresholds to diverge at unrelated rates. The limit measures are homogeneous in each component and finite on events where every component exceeds a positive level in absolute value somewhere on a compact window. We characterise convergence by anchor exceedance masses and conditional whole-path laws, together with a compact-window mass bound in the continuous-parameter setting. For fields indexed by a countable discrete abelian group or by R^m every shift-invariant tail measure in this class admits a strictly stationary realisation. Finite moving averages with shared volatility show that scalar row-tail measures and simultaneous-exceedance tail masses on every consecutive finite window can coincide while relative-lag tail masses differ.