I want to know if $\lim_{T-> \infty}$ of this$\frac{\sigma^{4}C_{H,K}^{2}}{4 T^{4HK}e^{2\theta T }}\int_{[0,T]^{4}}e^{\theta(t_{1}-s_{1})}e^{\theta(t_{2}-s_{2})}\left\vert(t_{1}t_{2})^{2H-1}(t_{1}^{2H}+t_{2}^{2H})^{K-2}+(2HK-1)\vert t_{1}-t_{2}\vert^{2HK-2}\right\vert\\ \times\left\vert(s_{1}s_{2})^{2H-1}(s_{1}^{2H}+s_{2}^{2H})^{K-2}+(2HK-1)\vert s_{1}-s_{2}\vert^{2HK-2}\right\vert dt_{1}ds_{1}dt_{2}ds_{2}$ with integral
$$ \frac{\sigma^{4}C_{H,K}^{2}}{4 T^{4HK}e^{2\theta T }}\\ \times \int\limits_{[0,T]^{4}}e^{\theta(t_{1}-s_{1})}e^{\theta(t_{2}-s_{2})}\left\vert(t_{1}t_{2})^{2H-1}(t_{1}^{2H}+t_{2}^{2H})^{K-2}+(2HK-1)\vert t_1-t_2\vert^{2HK-2} \right\vert\ \\ \times\left\vert(s_{1}s_{2})^{2H-1}(s_{1}^{2H}+s_{2}^{2H})^{K-2}+(2HK-1)\vert s_{1}-s_{2}\vert^{2HK-2}\right\vert dt_{1}ds_{1}dt_{2}ds_{2}$$ with 2HK>1 and H,K $\in$ (0,1) and $\theta>0$
is finite. Thanks to help me
