Random processes by example
著者
書誌事項
Random processes by example
World Scientific, c2014
大学図書館所蔵 件 / 全8件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 207-213) and index
内容説明・目次
内容説明
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 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 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.
目次
- Brief Reminder of Probability Theory
- Compound Poisson, Infinitely Divisible and Stable Random Variables
- Gaussian Processes: Wiener Process, Fractional Brownian Motion, Etc.
- Levy Processes
- Uncorrelated and Independently Scattered Random Measures and Respective Integrals
- Limit Theorems for Processes
- Teletraffic Workload Models: Weak Dependence, Long Range Dependence, Gaussian, Stable, and Intermediate Limits
- Kaj - Taqqu Telecom Processes
- Multivariate Workload Models.
「Nielsen BookData」 より