Asymptotic analysis of random walks : heavy-tailed distributions
著者
書誌事項
Asymptotic analysis of random walks : heavy-tailed distributions
(Encyclopedia of mathematics and its applications / edited by G.-C. Rota, [118])
Cambridge University Press, 2008
- : hardback
大学図書館所蔵 全51件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Series and series no. from jacket
Includes bibliographical references (p. 611-623) and index
内容説明・目次
内容説明
This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors.
目次
- Introduction
- 1. Preliminaries
- 2. Random walks with jumps having no finite first moment
- 3. Random walks with finite mean and infinite variance
- 4. Random walks with jumps having finite variance
- 5. Random walks with semiexponential jump distributions
- 6. Random walks with exponentially decaying distributions
- 7. Asymptotic properties of functions of distributions
- 8. On the asymptotics of the first hitting times
- 9. Large deviation theorems for sums of random vectors
- 10. Large deviations in the space of trajectories
- 11. Large deviations of sums of random variables of two types
- 12. Non-identically distributed jumps with infinite second moments
- 13. Non-identically distributed jumps with finite variances
- 14. Random walks with dependent jumps
- 15. Extension to processes with independent increments
- 16. Extensions to generalised renewal processes
- Bibliographic notes
- Index of notations
- Bibliography.
「Nielsen BookData」 より