Intersection of random sequences (Q579774)

Intersection of two random sequences is defined as a couple of identically distributed elements each belonging to a different sequence. A concept of a random sequence \(u_ n\) controlled by a random sequence \(v_ n\) is also introduced. Properties of different equivalent control sequences are investigated in terms of properties of their intersections. In particular, \textit{H. Thorisson}'s result [Adv. Appl. Probab. 15, 531- 561 (1983; Zbl 0512.60080)] concerning coupling of regenerative processes is generalized and interpreted by means of the intersection concept.