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Random Time Changes for Sock-Sorting and Other Stochastic Process Limit Theorems

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1.	Title	Title of document	Random Time Changes for Sock-Sorting and Other Stochastic Process Limit Theorems
2.	Creator	Author's name, affiliation, country	David Steinsaltz; University of California, Berkeley
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	maximal inequalities, decoupling, poissonization, functional central limit theorem, sorting, random allocations, auxiliary randomization, time change
3.	Subject	Subject classification	Primary: 60F17; Secondary: 60G70,60K30
4.	Description	Abstract	A common technique in the theory of stochastic process is to replace a discrete time coordinate by a continuous randomized time, defined by an independent Poisson or other process. Once the analysis is complete on this poissonized process, translating the results back to the original setting may be nontrivial. It is shown here that, under fairly general conditions, if the process $S_n$ and the time change $\phi_n$ both converge, when normalized by the same constant, to limit processes combined process $S_n(\phi_n(t))$ converges, when properly normalized, to a sum of the limit of the orginal process, and the limit of the time change multiplied by the derivative of $E S_n$. It is also shown that earlier results on the fine structure of the maxima are preserved by these time changes.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-05-20
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/51
10.	Identifier	Digital Object Identifier	10.1214/EJP.v4-51
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 4
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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