Persistence of Long-Range-Dependence Under Data Compression

One of the early motivations for current interest in the stochastic networks community in the study of network models involving long-range-dependent stochastic processes was the observation, based on statistical analysis of data, that variable-bit-rate video traffic over networks appears to exhibit long-range-dependent behavior. Such traffic is typically placed on the network after data compression algorithms are used on an underlying video source. It is natural to ask what role the data compression algorithm plays in the resulting long-range-dependent nature of the traffic.

Motivated by this question we study the entropy density of an underlying long-range-dependent process as a stochastic process in its own right, focusing on discrete time models. For classes of processes including renewal processes we prove that long-range-dependence of the underlying process implies long-range-dependence of the entropy density process, with the same Hurst exponent.

The underlying background in the data compression of stochastic processes, including the fundamental lemma of Barron relating the entropy density to data compression, and existing results for the short-range-dependent case that have the same flavor as our results, such as those due to Kontoyiannis, will also be discussed in this talk (joint work with Barlas Ou{g}uz.