A central limit theorem via differential equations

A central limit theorem via differential equations

Taral Guldahl Seierstad

Source: Ann. Appl. Probab. Volume 19, Number 2 (2009), 661-675.

Abstract

In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further conditions are satisfied, the parameters converge to a multivariate normal distribution.

First Page: Show

Primary Subjects: 60F05

Secondary Subjects: 05C80

Keywords: Central limit theorem; differential equations; random graphs; minimum degree graph process; d-process

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702246
Digital Object Identifier: doi:10.1214/08-AAP557
Zentralblatt MATH identifier: 05566096
Mathematical Reviews number (MathSciNet): MR2521884

back to Table of Contents

References

[1] Hurewicz, W. (1958). Lectures on Ordinary Differential Equations. The Technology Press of the Massachusetts Institute of Technology, Cambridge, MA.

Mathematical Reviews (MathSciNet): MR90703

[2] Kang, M. and Seierstad, T. G. (2007). Phase transition of the minimum degree random multigraph process. Random Structures Algorithms 31 330–353.

Mathematical Reviews (MathSciNet): MR2352179

[3] McLeish, D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Probab. 2 620–628.

Mathematical Reviews (MathSciNet): MR358933

Digital Object Identifier: doi:10.1214/aop/1176996608

[4] Ruciński, A. and Wormald, N. C. (1992). Random graph processes with degree restrictions. Combin. Probab. Comput. 1 169–180.

Mathematical Reviews (MathSciNet): MR1179247

Zentralblatt MATH: 0793.05113

[5] Tong, Y. L. (1990). The Multivariate Normal Distribution. Springer, New York.

Mathematical Reviews (MathSciNet): MR1029032

Zentralblatt MATH: 0689.62036

[6] Wormald, N. C. (1995). Differential equations for random processes and random graphs. Ann. Appl. Probab. 5 1217–1235.

Mathematical Reviews (MathSciNet): MR1384372

Zentralblatt MATH: 0847.05084

Digital Object Identifier: doi:10.1214/aoap/1177004612

Project Euclid: euclid.aoap/1177004612

[7] Wormald, N. C. (1999). The differential equation method for random graph processes and greedy algorithms. In Lectures on Approximation and Randomized Algorithms. (M. Karoński and H. J. Prömel, eds.) 75–152. PWN, Warsaw.

previous :: next