System Upgrade on Tue, May 28th, 2024 at 2am (EDT)
Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.
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 Lévy 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 Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of 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.
Sample Chapter(s)
Chapter 1: Preliminaries (367 KB)
Contents:
- Preliminaries:
- Random Variables: A Summary
- From Poisson to Stable Variables
- Limit Theorems for Sums and Domains of Attraction
- Random Vectors
- Random Processes:
- Random Processes: Main Classes
- Examples of Gaussian Random Processes
- Random Measures and Stochastic Integrals
- Limit Theorems for Poisson Integrals
- Lévy Processes
- Spectral Representations
- Convergence of Random Processes
- Teletraffic Models:
- A Model of Service System
- Limit Theorems for the Workload
- Micropulse Model
- Spacial Extensions
Readership: Graduate students and researchers in probability & statistics.
