4369 R. Arratia/Michael Waterman: An Erdo''s-Renyi law with shifts.
Adv. Math. 55 (1985), 13-23.

B. Gnedenko/V. Korolev: Random summation. CRC 1996, 270p. $80.
" ... allowing the number of summands to be a random number ...
This book, written by two grand masters of probability theory, gives
an up-to-date account of the theory, including many applications and
a substantial amount of new mathematical results. Well written and
carefully translated ... " (K. Sigmund)