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Weak convergence with random indices

Publication ,  Journal Article
Durrett, RT; Resnick, SI
Published in: Stochastic Processes and their Applications
January 1, 1977
Published version (DOI)

Suppose {Xnn≥-0} are random variables such that for normalizing constants an>0, bn, n≥0 we have Yn(·)=(X[n, ·]-bn/an ⇒ Y(·) in D(0.∞) . Then an and bn must in specific ways and the process Y possesses a scaling property. If {Nn} are positive integer valued random variables we discuss when YNn → Y and Y'n=(X[Nn]-bn)/an ⇒ Y'. Results given subsume random index limit theorems for convergence to Brownian motion, stable processes and extremal processes. © 1977.

Duke Scholars

Richard Timothy Durrett
Author Richard Timothy Durrett Mathematics

Published In

Stochastic Processes and their Applications

DOI

10.1016/0304-4149(77)90031-X

ISSN

0304-4149

Publication Date

January 1, 1977

Volume

5

Issue

3

Start / End Page

213 / 220

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Durrett, R. T., & Resnick, S. I. (1977). Weak convergence with random indices. Stochastic Processes and Their Applications, 5(3), 213–220. https://doi.org/10.1016/0304-4149(77)90031-X
Durrett, R. T., and S. I. Resnick. “Weak convergence with random indices.” Stochastic Processes and Their Applications 5, no. 3 (January 1, 1977): 213–20. https://doi.org/10.1016/0304-4149(77)90031-X.
Durrett RT, Resnick SI. Weak convergence with random indices. Stochastic Processes and their Applications. 1977 Jan 1;5(3):213–20.
Durrett, R. T., and S. I. Resnick. “Weak convergence with random indices.” Stochastic Processes and Their Applications, vol. 5, no. 3, Jan. 1977, pp. 213–20. Scopus, doi:10.1016/0304-4149(77)90031-X.
Durrett RT, Resnick SI. Weak convergence with random indices. Stochastic Processes and their Applications. 1977 Jan 1;5(3):213–220.
Journal cover image

Published In

Stochastic Processes and their Applications

DOI

10.1016/0304-4149(77)90031-X

ISSN

0304-4149

Publication Date

January 1, 1977

Volume

5

Issue

3

Start / End Page

213 / 220

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics