论文标题
多元亚临界分支过程在随机环境中的属性
Properties of multitype subcritical branching processes in random environment
论文作者
论文摘要
我们研究$ p-$类型的亚临界分支过程在随机环境中以零时为零的随机环境中的属性，由不同类型的颗粒的粒子$ \ left（z__ {1}，..，z_ {1}，..，z_ {p} \ right）$ \。假设该过程属于所谓的强度亚临界过程的类别，我们表明，它的生存概率$ n $ \的行为对大$ n $ \ as $ c（\ mathbf {z}）λ^{n} $ \ $ c（\ mathbf {z}）$λ$ \是$λ$ \是均值$ n是均值的$ n是均值$ c的$ c。 \是一个明确给出的常数。我们还证明，在长期使用该过程的生存的情况下，粒子数量的有限条件分布不取决于启动该过程的粒子数量的向量$ \ mathbf {z} $。
We study properties of a $p-$type subcritical branching process in random environment initiated at moment zero by a vector $\mathbf{z}=\left( z_{1},..,z_{p}\right) $\ of particles of different types. Assuming that the process belongs to the class of the so-called strongly subcritical processes we show that its survival probability to moment $n$\ behaves for large $n$\ as $C(\mathbf{z})λ^{n}$\ where $λ$\ is the upper Lyapunov exponent for the product of mean matrices of the process and $C(\mathbf{z})$% \ is an explicitly given constant. We also demonstrate that the limiting conditional distribution of the number of particles given the survival of the process for a long time does not depend on the vector $\mathbf{z}$ of the number of particles initiated the process.
