SOME PROPERTIES OF A RANDOM LINEAR DIFFERENCE EQUATION1
- 26 February 1983
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 25 (2) , 345-357
- https://doi.org/10.1111/j.1467-842x.1983.tb00388.x
Abstract
Summary: Some simple conditions are given for the absolute continuity of the limiting distribution of a random linear difference equation. These results are applied to the super‐critical Bellman‐Harris branching process with immigration. When the coefficients of the difference equation are non‐negative and there is no limiting distribution, it is shown that the asymptotic behaviour of the solutions is the same as that of the partial sums of a divergent random power series. A number of limit theorems are given for the latter situation.Keywords
This publication has 9 references indexed in Scilit:
- Stationarity and invertibility of simple bilinear modelsStochastic Processes and their Applications, 1982
- On the first-order bilinear time series modelJournal of Applied Probability, 1981
- On a stochastic difference equation and a representation of non–negative infinitely divisible random variablesAdvances in Applied Probability, 1979
- Limit theorems for the simple branching process allowing immigration, II. The case of infinite offspring meanAdvances in Applied Probability, 1979
- Regularly Varying FunctionsLecture Notes in Mathematics, 1976
- On the Continuity of the Distribution of a Sum of Dependent Variables Connected with Independent Walks on LinesTheory of Probability and Its Applications, 1974
- Supercritical age-dependent branching processes with immigrationStochastic Processes and their Applications, 1974
- Random geometric series and intersymbol interferenceIEEE Transactions on Information Theory, 1973
- On the Supercritical One Dimensional Age Dependent Branching ProcessesThe Annals of Mathematical Statistics, 1969