Weak convergence with random indices
Publication
, Journal Article
Durrett, RT; Resnick, SI
Published in: Stochastic Processes and their Applications
January 1, 1977
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
Published In
Stochastic Processes and their Applications
DOI
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
APA
Chicago
ICMJE
MLA
NLM
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.
Published In
Stochastic Processes and their Applications
DOI
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