论文标题
双性恋加尔顿 - 瓦特森流程的缩放限制
Scaling limits of bisexual Galton-Watson processes
论文作者
论文摘要
双性恋Galton-Watson过程是离散的马尔可夫链，在这些链中，繁殖事件是由于男性和女性的交配而引起的。由于这种相互作用，Galton-Watson过程的标准分支属性丢失了。我们证明了基于Bansaye，Caballero和M {é} L {é} ARD开发的最新技术，证明了方便地重新恢复双性恋的Galton-Watson工艺。我们还确定这些重新定制过程的可能限制是随机系统的解决方案，通过以托管术语为单数系数将两个方程式耦合到方形根部，作为布朗运动的系数。在一些额外的集成性假设下，可以获得这种随机微分方程的限制系统的路径唯一性以及重新定制过程的收敛性。考虑了两个与相互保真度相对应的例子。
Bisexual Galton-Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching property of Galton-Watson processes is lost. We prove tightness for conveniently rescaled bisexual Galton-Watson processes, based on recent techniques developed by Bansaye, Caballero and M{é}l{é}ard. We also identify the possible limits of these rescaled processes as solutions of a stochastic system, coupling two equations through singular coefficients in Poisson terms added to square roots as coefficients of Brownian motions. Under some additional integrability assumptions, pathwise uniqueness of this limiting system of stochastic differential equations and convergence of the rescaled processes are obtained. Two examples corresponding to mutual fidelity are considered.
