東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Nonlinear Hawkes Processes.

Zhu, Lingjiong.

FindBook

Google Book

Amazon

博客來

Nonlinear Hawkes Processes.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Nonlinear Hawkes Processes./
作者:	Zhu, Lingjiong.
面頁冊數:	218 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
Contained By:	Dissertation Abstracts International74-12B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3591369
ISBN:	9781303319426

Nonlinear Hawkes Processes.
Zhu, Lingjiong.

Nonlinear Hawkes Processes. - 218 p.

Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.

Thesis (Ph.D.)--New York University, 2013.

The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are applications in finance, neuroscience, genome analysis, seismology, sociology, criminology and many other fields. We first survey the known results about the theory and applications of both linear and nonlinear Hawkes processes. Then, we obtain the central limit theorem and process-level, i.e. level-3 large deviations for nonlinear Hawkes processes. The level-1 large deviation principle holds as a result of the contraction principle. We also provide an alternative variational formula for the rate function of the level-1 large deviations in the Markovian case. Next, we drop the usual assumptions on the nonlinear Hawkes process and categorize it into different regimes, i.e. sublinear, sub-critical, critical, super-critical and explosive regimes. We show the different time asymptotics in different regimes and obtain other properties as well. Finally, we study the limit theorems of linear Hawkes processes with random marks.

ISBN: 9781303319426Subjects--Topical Terms:

515831
Mathematics.

Nonlinear Hawkes Processes.
LDR:02052nam a2200301 4500 001 1964105
005 20141010091529.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303319426
035 $a (MiAaPQ)AAI3591369
035 $a AAI3591369
040 $a MiAaPQ $c MiAaPQ
100 1 $a Zhu, Lingjiong. $3 2100493
245 1 0 $a Nonlinear Hawkes Processes.
300 $a 218 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
500 $a Adviser: S. R. S. Varadhan.
502 $a Thesis (Ph.D.)--New York University, 2013.
520 $a The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are applications in finance, neuroscience, genome analysis, seismology, sociology, criminology and many other fields. We first survey the known results about the theory and applications of both linear and nonlinear Hawkes processes. Then, we obtain the central limit theorem and process-level, i.e. level-3 large deviations for nonlinear Hawkes processes. The level-1 large deviation principle holds as a result of the contraction principle. We also provide an alternative variational formula for the rate function of the level-1 large deviations in the Markovian case. Next, we drop the usual assumptions on the nonlinear Hawkes process and categorize it into different regimes, i.e. sublinear, sub-critical, critical, super-critical and explosive regimes. We show the different time asymptotics in different regimes and obtain other properties as well. Finally, we study the limit theorems of linear Hawkes processes with random marks.
590 $a School code: 0146.
650 4 $a Mathematics. $3 515831
650 4 $a Economics, Finance. $3 626650
650 4 $a Statistics. $3 517247
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0508
690 $a 0463
690 $a 0364
710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 74-12B(E).
790 $a 0146
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3591369