摘要:
假设{Y(t);t ≥0}是带移民的连续时间分枝过程，其中分枝概率是{b
k;k≥0}，移民概率是{a
j;j≥0}。令b
0=0，0 < b
k≠1(k≥1)，1 < m=Σ
k=0∞kb
k < ∞，0 < a=Σ
j=0∞jb
j < ∞和
。首先，我们证明
是一个上鞅并且收敛到随机变量K。然后，我们在α > 0和ε > 0时，当{b
k;k≥0}和{a
k;k≥0}满足多种矩条件，研究P(|K(t)-K| > ε)在t趋于无穷时的衰减速率。
Abstract:
Suppose {Y(t);t ≥0} is the continuous time supercritical branching process with offspring rates {b
k;k≥0} and immigration rates {a
j;j≥0}. Let b
0=0, 0 < b
k≠1(k≥1),1 < m=Σ
k=0∞ kb
k < ∞, 0 < a=Σ
j=0∞ jb
j < ∞ and
. Firstly, we suppose that
is a sub-martingale and converges to a random variable K. Then we study the decay rates of P(|K(t)-K| > ε) as t→∞ for α > 0, ε > 0 under various moment conditions on {a
k;k≥0} and {b
k;k≥0}.