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PDF(456 KB)
PDF(456 KB)
一类随机环境中多维分枝过程的极限理论
The Limit Theory of One Kind of Multi-branching Process in Random Environment
本文根据粒子的适应度定义了一类随机环境中的多维分枝过程，研究了它的母函数，给出了母函数的递推关系式.同时计算了过程的期望和方差，类似Galton—Watson过程，讨论了它的灭绝概率，构造了一个非负鞅Wn，并在子孙分布一阶矩和二阶矩有界的情况下证明了Wn依L2收敛.
We defined a multi-branching process in varying environment by it's fitness. We studied the properties of its generating function and gave the recurrence relation of the generating function. We calculated the expectation and variance of the process, just like Galton-Watson process, we studied its extinction probability and constructed a nonnegative martingale, in the case that the first and second order moments of offspring are bounded, we also proved that this martingale converged in L2.
随机环境 / 多维分枝过程 / 母函数 / 极限 {{custom_keyword}} /
random environment / multi-branching / generating function / limit {{custom_keyword}} /
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国家自然科学基金资助项目（11371321，11601260）；山东省中青年科学家奖励基金（ZR2016AB01）；浙江工商大学人文社科统计学基地资助项目
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