Necessary Conditions in Limit Theorems for Cumulative Processes
P. W. Glynn and W. Whitt
Stochastic Processes and their Applications, Vol. 98 (2), 199-209 (2002)
We show that su,cient conditions in terms ofmoments for cumulative processes (additive functionals of regenerative processes) to satisfy the central limit theorem and the weak law of large numbers established in Glynn and Whitt (Stochastic Process. Appl. 47 (1993) 299–314) are also necessary, as previously conjectured.