Multivariate Extreme Values for Dynamical Systems

The candidate solution follows the paper’s declustering/big-blocks–small-gaps scheme under conditions Д(un) and Д′(un), and correctly derives lim μ(Mn ≤ un(τ)) = exp(−θ(τ) Γ̂(τ)). It also matches the paper’s handling of error terms via n γ(q,n,t_n) and the Δ^(q) anti-clustering sum. One minor gap is that the model’s Step 5 appeals to G(cτ) = (G(τ))^c without proof; the paper instead proves θ(cτ)=θ(τ) via a time-change argument and then deduces homogeneity. This is easily patched by adopting the paper’s argument. Aside from this, the proofs are essentially the same.