关于共生分枝模型的矩和界面
On the moments and the interface of the symbiotic branching model
摘要：
本文引入了Etheridge和Fleischmann [随机过程]提出的共生分枝模型中分离矩渐近行为的临界曲线。114（2004）127- 160]分为两种制度。利用基于两种不同对偶的参数和Spitzer [trans.Amer.Math.Soc.87（1958）187- 197]关于平面布朗运动从楔形体的出射时刻的经典结果，我们证明了控制模型的参数提供了由次指数增长分离的有界和指数增长矩的区域。当时间趋于无穷大时，力矩与极限分布密切相关。极限分布可以通过自对偶性论证来导出，该论证扩展了Dawson和Perkins的结果[Ann. Probab. 26（1998）1088- 1138]的相互催化支化模型。作为一个应用，我们给出了35阶矩的界如何改进Etheridge和Fleischmann [随机过程]的结果. 114（2004）127- 160]关于共生分枝模型的界面的传播速度。
英文摘要：
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 [Stochastic Process. Appl. 114 (2004) 127--160] into two regimes. Using arguments based on two different dualities and a classical result of Spitzer [Trans. Amer. Math. Soc. 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 [Ann. Probab. 26 (1998) 1088--1138] for the mutually catalytic branching model. As an application, we show how a bound on the 35th moment improves the result of Etheridge and Fleischmann [Stochastic Process. Appl. 114 (2004) 127--160] on the speed of the propagation of the interface of the symbiotic branching model.
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