Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155779 | Stochastic Processes and their Applications | 2011 | 21 Pages |
Abstract
We investigate the long-term behaviour of a system of SDEs for dâ¥2 types, involving catalytic branching and mutation between types. In particular, we show that the overall sum of masses converges to zero but does not hit zero in finite time a.s. We shall then focus on the relative behaviour of types in the limit. We prove weak convergence to a unique stationary distribution that does not put mass on the set where at least one of the coordinates is zero. Finally, we provide a complete analysis of the case d=2.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
S. Kliem,