| EPSRC Reference: |
GR/J76187/01 |
| Title: |
SUPERCRITICAL BRANCHING PROCESS; NON-TRIVIAL LIMITS AND THEIR TAIL BEHAVIOUR |
| Principal Investigator: |
Biggins, Professor JD |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Probability and Statistics |
| Organisation: |
University of Sheffield |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
26 September 1994 |
Ends: |
02 March 1996 |
Value (£): |
60,762
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| EPSRC Research Topic Classifications: |
| Statistics & Appl. Probability |
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Summary on Grant Application Form |
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Two main directions, both motivated by recent work on constructing diffusions and similar processes on fractals, are envisaged. (i) Results on the tail of W, the limit of the normalized population size in a branching process, will be extended and refined. The refinement of existing results will involve improving the large deviation asymptotics, whilst the extensions will seek similar results for branching processes with extra structure (eg multitype, varying environment). The similarities of the problem with some of those studied in the combinatorial enumeration literature will be exploited.(ii) The convergence of the normalized population size to a non-degenerate limit in various generalizations of the simple branching process will be considered. The emphasis will be on seeking conditions that are natural (in the light of what is known about the simple branching process). Such results would have application in the construction of diffusion on fractals. Several contributions to that literature contain particular branching process results that should be refined.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.shef.ac.uk |