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Nuclear space-valued stochastic diff...

The University of Iowa.

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Nuclear space-valued stochastic differential equations driven by Poisson random measures.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Nuclear space-valued stochastic differential equations driven by Poisson random measures./
Author:	Xiong, Jie.
Description:	170 p.
Notes:	Director: Gopinath Kallianpur.
Contained By:	Dissertation Abstracts International53-07B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9235050

Nuclear space-valued stochastic differential equations driven by Poisson random measures.
Xiong, Jie.

Nuclear space-valued stochastic differential equations driven by Poisson random measures. - 170 p.

Director: Gopinath Kallianpur.

Thesis (Ph.D.)--The University of Iowa, 1992.

The above problems are motivated by applications to neurophysiology, in particular, to the fluctuation of voltage potentials of spatially distributed neurons and to the study of asymptotic behavior of large systems of interacting neurons.Subjects--Topical Terms:

517247
Statistics.

Nuclear space-valued stochastic differential equations driven by Poisson random measures.
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005 20100701
008 100701s1992 ||||||||||||||||| ||eng d
035 $a (UMI)AAI9235050
035 $a AAI9235050
040 $a UMI $c UMI
100 1 $a Xiong, Jie. $3 906722
245 1 0 $a Nuclear space-valued stochastic differential equations driven by Poisson random measures.
300 $a 170 p.
500 $a Director: Gopinath Kallianpur.
500 $a Source: Dissertation Abstracts International, Volume: 53-07, Section: B, page: 3581.
502 $a Thesis (Ph.D.)--The University of Iowa, 1992.
520 $a The above problems are motivated by applications to neurophysiology, in particular, to the fluctuation of voltage potentials of spatially distributed neurons and to the study of asymptotic behavior of large systems of interacting neurons.
520 $a When the magnitudes of the driving terms are small enough and the Poisson streams occur frequently enough, it is proved that the stochastic differential equations mentioned above can be approximated by diffusion equations.
520 $a The thesis is devoted primarily to the study of stochastic differential equations on duals of nuclear spaces driven by Poisson random measures. The existence of a weak solution is obtained by the Galerkin method and the uniqueness is established by implementing the Yamada-Watanabe argument in the present setup.
520 $a Finally, we consider a system of interacting stochastic differential equations driven by Poisson random measures. Let $\rm (X\sbsp{1}{n}(t),\cdots,X\sbsp{n}{n}(t))$ be the solution of this system and consider the empirical measures $$\rm\zeta\sb{n}(\omega,B) \equiv {1\over n}\sum\limits\sbsp{j=1}{n}\delta\sb{X\sbsp{j}{n}(\cdot,\omega)}(B)\qquad (n \ge 1).$ $i t is proved that $\zeta\sb{\rm n}$ converges in distribution to a non-random measure which is the unique solution of a McKean-Vlasov equation.
590 $a School code: 0096.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a The University of Iowa. $3 1017439
773 0 $t Dissertation Abstracts International $g 53-07B.
790 $a 0096
790 1 0 $a Kallianpur, Gopinath, $e advisor
791 $a Ph.D.
792 $a 1992
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9235050