Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T07:37:16.202Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple random walk statistics. Part II: Continuous time results

Part of: Nonparametric inference Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

W. Böhm  and
W. Panny
W. Böhm*
Affiliation:
University of Economics, Vienna
W. Panny*
Affiliation:
University of Economics, Vienna
*
∗Postal address: Department of Statistics, University of Economics, Augasse 2–6, A-1090 Wien, Austria.
∗Postal address: Department of Statistics, University of Economics, Augasse 2–6, A-1090 Wien, Austria.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper various statistics for randomized random walks and their distributions are presented. The distributional results are derived by means of a limiting procedure applied to the pertaining discrete time process, which has been considered in part I of this work (Katzenbeisser and Panny 1996). This basic approach, originally due to Meisling (1958), seems to offer certain technical advantages, since it avoids the use of Laplace transforms and is even simpler than Feller's randomization technique.

Keywords

RANDOMIZED RANDOM WALKSLATTICE PATHSRANK ORDER STATISTICS

MSC classification

Secondary: 62G30: Order statistics; empirical distribution functions 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 331 - 339
Copyright
Copyright © Applied Probability Trust 1996 

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.)

References

Böhm, W. and Mohanty, S. G. (1990) Discretization of Markovian queueing systems. Technical Report. Department of Mathematical Statistics, University of Economics, Vienna.Google Scholar
Böhm, W. and Mohanty, S. G. (1993) The transient solution of M/M/1 queues under (M, N)-policy. A combinatorial approach. T Stat. Plann. Inference 34, 23–33.Google Scholar
Böhm, W. and Mohanty, S. G. (1994) On discrete time Markovian N-policy queues involving batches. Sankhya A 56, 1–20.Google Scholar
Dwass, M. (1967) Simple random walk and rank order statistics. Ann. Math. Statist. 38, 1042–1053.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications. Vol. 2, 2nd. edn. Wiley, New York.Google Scholar
Sen, Kanwar, Jain, J. L. and Gupta, J. M. (1993) Lattice path approach to transient solution of M/M/1 with (0, K) control policy. J. Stat. Plann. Inference 34, 259–268.Google Scholar
Katzenbeisser, W. and Panny, W. (1996) Simple random walk statistics. Part I: Discrete time results. J. Appl. Prob. 33, 311–330.Google Scholar
Jain, J. L. and Gupta, J. M. (1993) Combinatorial approach to Markovian queues. J. Stat. Plann. Inference 34, 269–280.Google Scholar
Meisling, T. (1958) Discrete-time queueing theory. J. Operat. Res. Soc. Am. 6, 96–105.Google Scholar
Mohanty, S. G. and Panny, W. (1989) A discrete-time analogue of the M/M/1 queue and the transient solution: An analytic approach. In Limit Theorems in Probability and Statistics. Pécs (Hungary), Colloq. Math. Soc. Janos Bolyai 57, 417–124.Google Scholar
Mohanty, S. G. and Panny, W. (1990) A discrete-time analogue of the M/M/1 queue and the transient solution: A geometric approach. Sankhya A, 52, 364–370.Google Scholar
Mohanty, S. G., Parthasarathy, P. R. and Sharaf Ali, M. (1990) On the transient solution of a discrete queue. Technical Report. Mathematics and Statistics Department, McMaster University, Hamilton.Google Scholar