Extremal Processes Increasing Processes with Independent Increments Weak Limit Theorems Levy Measure Poisson Point Processes Bernoulli Point Processes Random Sample Size
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 35, No 2, (2009), 169p-194p
We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d
as well as for the associated with it sum and extremal processes on an open subset S . The complement
of S turns out to be the explosion area of the limit Poisson point process.
In order to prove our criterion for weak convergence of the sum processes we introduce and study
sum processes over explosion area. Finally we generalize the model of u.n.t.a. to random sample size processes.