CONDITIONED LIMIT THEOREMS FOR FUNCTIONS OF THE AVERAGEOF I.I.D. RANDOM VARIABLES
A. Szubarga D. Szynal
Abstract: Let be a sequence of i.i.d. random variables with
Form the random walk by setting
Let denote the hitting time of the set by
the random walk. Put Let be a real-valued,
right-continuous function on having left limits, with and continuous at
For we define the map by
Put This note deals with the asymptotic behaviour of
conditioned on Moreover, we investigate the asymptotic behaviour in the
question when n is replaced by where is a sequence of positive
integer-valued random variables.