On the moments and the interface of the symbiotic branching model
<p>In this paper we introduce a critical curve separating the asymptotic behavior of the moments of the symbiotic branching model, introduced by Etheridge and Fleischmann [<em>Stochastic Process. App.</em> 114 (2004) 127-160] into two regimes. Using arguments based on two different...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics
2011
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| _version_ | 1797072847534817280 |
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| author | Blath, J Döring, L Etheridge, A |
| author_facet | Blath, J Döring, L Etheridge, A |
| author_sort | Blath, J |
| collection | OXFORD |
| description | <p>In this paper we introduce a critical curve separating the asymptotic behavior of the moments of the symbiotic branching model, introduced by Etheridge and Fleischmann [<em>Stochastic Process. App.</em> 114 (2004) 127-160] into two regimes. Using arguments based on two different dualities and a classical result of Spitzer [<em>Trans. Amer. Math. Soc.</em> 87 (1958) 187-197] on the exit-time of a planar Brownian motion from a wedge, we prove that the parameter governing the model provides regimes of bounded and exponentially growing moments separated by subexponential growth. The moments turn out to be closely linked to the limiting distribution as time tends to infinity. The limiting distribution can be derived by a self-duality argument extending a result of Dawson and Perkins [<em>Ann. Probab.</em> 26 (1998) 1088-1138] for the mutually catalytic branching model.</p><p>As an application, we show how a bound on the 35th moment improves the result of Etheridge and Fleischmann [<em>Stochastic Process. Appl.</em> 114 (2004) 127-160] on the speed of the propagation of the the interface of the symbiotic branching model.</p> |
| first_indexed | 2024-03-06T23:13:34Z |
| format | Journal article |
| id | oxford-uuid:66562734-a643-4b05-9201-4a4421f48998 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:13:34Z |
| publishDate | 2011 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:66562734-a643-4b05-9201-4a4421f489982022-03-26T18:31:14ZOn the moments and the interface of the symbiotic branching modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:66562734-a643-4b05-9201-4a4421f48998ProbabilityStatistics (see also social sciences)EnglishOxford University Research Archive - ValetInstitute of Mathematical Statistics2011Blath, JDöring, LEtheridge, A<p>In this paper we introduce a critical curve separating the asymptotic behavior of the moments of the symbiotic branching model, introduced by Etheridge and Fleischmann [<em>Stochastic Process. App.</em> 114 (2004) 127-160] into two regimes. Using arguments based on two different dualities and a classical result of Spitzer [<em>Trans. Amer. Math. Soc.</em> 87 (1958) 187-197] on the exit-time of a planar Brownian motion from a wedge, we prove that the parameter governing the model provides regimes of bounded and exponentially growing moments separated by subexponential growth. The moments turn out to be closely linked to the limiting distribution as time tends to infinity. The limiting distribution can be derived by a self-duality argument extending a result of Dawson and Perkins [<em>Ann. Probab.</em> 26 (1998) 1088-1138] for the mutually catalytic branching model.</p><p>As an application, we show how a bound on the 35th moment improves the result of Etheridge and Fleischmann [<em>Stochastic Process. Appl.</em> 114 (2004) 127-160] on the speed of the propagation of the the interface of the symbiotic branching model.</p> |
| spellingShingle | Probability Statistics (see also social sciences) Blath, J Döring, L Etheridge, A On the moments and the interface of the symbiotic branching model |
| title | On the moments and the interface of the symbiotic branching model |
| title_full | On the moments and the interface of the symbiotic branching model |
| title_fullStr | On the moments and the interface of the symbiotic branching model |
| title_full_unstemmed | On the moments and the interface of the symbiotic branching model |
| title_short | On the moments and the interface of the symbiotic branching model |
| title_sort | on the moments and the interface of the symbiotic branching model |
| topic | Probability Statistics (see also social sciences) |
| work_keys_str_mv | AT blathj onthemomentsandtheinterfaceofthesymbioticbranchingmodel AT doringl onthemomentsandtheinterfaceofthesymbioticbranchingmodel AT etheridgea onthemomentsandtheinterfaceofthesymbioticbranchingmodel |