论文标题
限制与移民的连续分支过程的时间平均定理
Limit theorems for time averages of continuous-state branching processes with immigration
论文作者
论文摘要
在这项工作中，我们调查了时间平均过程$ \ left的限制定理（\ frac {1} {t} \ int_0^t x_s^x_s^x ds \ right）_ {t \ geq 0} $，其中$ x^x $是$ x^x $是一个亚临界连续分支与移民（cbi Crocesses $ cbi Crossices）$ x的$ x 0 $ x的$ x.在分支和移民措施的第二刻条件下，我们首先证明了$ l^2 $的大量法律，然后确定了中心限制定理。另外，假设分支和移民措施的大跳跃具有某些顺序的有限指数力矩，我们在主要结果中证明了大偏差原理，并在分支和移民机制方面为良好的利率功能提供了半明确的表达。我们的方法深入基于对时间平均过程的相应广义riccati方程和相关指数力矩的详细研究。
In this work we investigate limit theorems for the time-averaged process $\left(\frac{1}{t}\int_0^t X_s^x ds\right)_{t\geq 0}$ where $X^x$ is a subcritical continuous-state branching processes with immigration (CBI processes) starting in $x \geq 0$. Under a second moment condition on the branching and immigration measures we first prove the law of large numbers in $L^2$ and afterward establish the central limit theorem. Assuming additionally that the big jumps of the branching and immigration measures have finite exponential moments of some order, we prove in our main result the large deviation principle and provide a semi-explicit expression for the good rate function in terms of the branching and immigration mechanisms. Our methods are deeply based on a detailed study of the corresponding generalized Riccati equation and related exponential moments of the time-averaged process.
