STRONG LIMIT THEOREMS FOR GENERAL RENEWAL PROCESSES
Oleg Klesov
Zdzisław Rychlik
Josef Steinebach
Abstract: An approach is discussed to derive strong limit theorems for general renewal
processes from the corresponding asymptotics of the underlying renewal sequence. Neither
independence nor stationarity of increments is required. In certain situations, just the dualities
between the renewal processes and their defining sequences in combination with some
regularity conditions on the normalizing constants are sufficient for the proofs.
There are other cases, however, in which the duality arguments do not apply, and
where other techniques have to be developed. Finally, there are also examples, in
which an inversion of the limit theorems under consideration cannot work at all.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -