Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T05:13:59.722Z Has data issue: false hasContentIssue false
  • English
  • Français

On the rate of convergence of some functionals of a stochastic process

Published online by Cambridge University Press:  14 July 2016

S. Rachev  and
P. Todorovic
S. Rachev
Affiliation:
University of California, Santa Barbara
P. Todorovic*
Affiliation:
University of California, Santa Barbara
*
∗ Postal address for both authors: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with the rate of convergence of certain functionals associated with a stochastic process arising in the modelling of soil erosion. Some limit theorems are derived for the total crop production Sn over a number n of years, and the rate of convergence of Sn to its limit S is discussed. Some stability assumptions are considered, and particular stable geometric infinitely divisible processes analyzed.

Keywords

LIMITING DISTRIBUTIONSTABLE PROCESSINFINITELY DIVISIBLE PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 805 - 814
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by NSF Grant DMS-8902330.

References

[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
[2] Basu, A. P., Ebrahimi, N. and Klefsjo, B. (1983) Multivariate harmonic new better than used in expectation distribution. Scand. J. Statist Theory Appl. 10.Google Scholar
[3] Basu, A. P. and Ebrahimi, N. (1985) Testing whether survival function is harmonic new better than used in expectation. Ann. Inst. Statist. Math. 37, Ser. A, 347–359.CrossRefGoogle Scholar
[4] De Haan, L. (1984) A spectral representation for max-stable processes. Ann. Prob. 12, 1194–1204.Google Scholar
[5] De Haan, L. and Resnick, S. I. (1977) Limit theory for multivariate samples extremes. Z. Wahrscheinlichkeitsth. 40, 317–333.CrossRefGoogle Scholar
[6] Kalashnikov, V. V. and Rachev, S. T. (1988) Mathematical Methods for Construction for Queueing Models. Nauka, Moscow (in Russian). English transl. (1990) Wadsworth and Brooks Cole.Google Scholar
[7] Klebanov, L. B., Maniya, G. M. and Melamed, I. A. (1984) A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables. Theory Prob. Appl. 29, 791–794.CrossRefGoogle Scholar
[8] Puri, P. S. (1987) On almost sure convergence of an erosion process due to Todorovic and Gani. J. Appl. Prob. 24, 1001–1005.CrossRefGoogle Scholar
[9] Rachev, S. T. (1984) The Monge–Kantorovich mass transference problem and its stochastic applications. Theory Prob. Appl. 29, 647–676.CrossRefGoogle Scholar
[10] Todorovic, P., Woolhiser, D. A. and Renard, K. G. (1987) Mathematical model for evaluation of the effect of soil erosion on crop productivity. Hydrolog. Process. 1, 181–198.CrossRefGoogle Scholar
[11] Todorovic, P. and Gani, J. (1987) Modeling of the effect of erosion on crop production. J. Appl. Prob. 24, 787–797.CrossRefGoogle Scholar
[12] Todorovic, P. (1987) An extremal problem arising in soil erosion modeling. In Applied Probability, Stochastic Processes and Sampling Theory, ed. MacNeil, I. B. and Umphrey, G. J., Reidel, Dordrecht, 65–73.CrossRefGoogle Scholar
[13] Zolotarev, S. T. (1983) Probability metrics. Theory Prob. Appl. 28, 278–307.CrossRefGoogle Scholar