Subcritical multitype Markov branching processes with immigration generated by Poisson random measures.

We investigate multitype subcritical Markov branching processes with immigration driven by Poisson random measures. Limiting distributions are established for various rates of the Poisson measures when they are asymptotically equivalent to exponential or regularly varying functions. Results analogous to a strong LLN are proved, and limiting normal distributions are obtained when the local intensity of the Poisson measure increases with time. When it decreases, conditional limiting distributions are established. When the intensity converges to a constant, a stationary limiting distribution is obtained. The asymptotic behavior of the first and second moments of the processes is also investigated. [ABSTRACT FROM AUTHOR]

Copyright of Communications in Statistics: Theory & Methods is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)