Limit theorems for extremal processes generated by a point process with correlated time and space components

The point process N={(Tk,Xk),k=0,1,2,3…}N={(Tk,Xk),k=0,1,2,3…} defines the sequence of maxima M(t)=⋁{k:Tk≤t}XkM(t)=⋁{k:Tk≤t}Xk. Using time and space scaling it is possible to define different sequences of random time changed extremal processes. The convergence of such sequences to nondegenerate extremal processes is proved in case where the time and space components of the point process are correlated.