}$$ where $\gamma_0(u)\to 0$, as $u\rightarrow \infty$. Hence, $$\label{upper bound around maximum 0} \begin{split} &\limsup_{u\rightarrow \infty}\frac{\mathbb{P}\left(\bigcup_{(s,t)\in \mathcal{D}} \{X_0(s)>u, X_0(t)>u)\}\right)}{u^{N(\frac{0}{\alpha_0}+\frac{0}{\alpha_0}-0)}\Psi(u,\rho)}\\ &\leq (0\pi)^{\frac{N}{0}}(-r''(0))^{-\frac{N}{0}}(0+\rho)^N mes_N(A_0\cap A_0)