Open Access
1999 Random Time Changes for Sock-Sorting and Other Stochastic Process Limit Theorems
David Steinsaltz
Author Affiliations +
Electron. J. Probab. 4: 1-25 (1999). DOI: 10.1214/EJP.v4-51


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.


Download Citation

David Steinsaltz. "Random Time Changes for Sock-Sorting and Other Stochastic Process Limit Theorems." Electron. J. Probab. 4 1 - 25, 1999.


Accepted: 20 May 1999; Published: 1999
First available in Project Euclid: 4 March 2016

zbMATH: 0929.60023
MathSciNet: MR1692672
Digital Object Identifier: 10.1214/EJP.v4-51

Primary: 60F17
Secondary: 60G70 , 60K30

Keywords: auxiliary randomization , Decoupling , functional central limit theorem , Maximal inequalities , poissonization , random allocations , sorting , Time change

Vol.4 • 1999
Back to Top