Invariance properties of the negative binomial Levy process and stochastic self-similarity.

In English We study the concept of self-similarity with respect to stochastic
time change. The negative binomial process (NBP) is an example of a
family of random time transformations with respect to which stochastic
self-similarity holds for certain stochastic processes. These processes
include gamma process, geometric stable processes, Laplace motion, and
fractional Laplace motion. We derive invariance properties of the NBP
with respect to random time deformations in connection with stochastic
self-similarity. In particular, we obtain more general classes of processes
that exhibit stochastic self-similarity properties. As an application, our
results lead to approximations of the gamma process via the NBP and
simulation algorithms for both processes.