Random Processes by Example

Next, it illustrates general concepts by handling a transparent but rich example of a teletraffic model . A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Levy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit completely different applied interpretations.

The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.