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By vertical and horizontal re-scaling, without loss of generality $a_1=a_2=1$, so that $$EX_sX_t=1-|t-s|\quad\text{if}\quad|t-s|\le u,$$ where $u\in(0,1)$. Take any $h\in(0,1)$ and let $$U_t:=\frac1{\sqrt2}\,(X_{(1-h)t}+Y_{(1+h)t}),$$ where $(Y_t)$ is an independent copy of $(X_t)$. Then $$EU_sU_t=1-|t-s|=EX_sX_t\quad\text{if}\quad|t-s|\le u/(1+h),$$ as desired.