论文标题
标记点过程和对标记鹰派过程的应用的准假性分析
Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes
论文作者
论文摘要
我们为一类多变量标记的点过程制定了准类分析程序。作为一般方法的一种副产品，我们在稳定性和终身性条件下建立了准log可能性的局部渐近正态性，以及准类似和准 - 巴比耶斯估计量的瞬间的收敛性。为了说明通用方法，我们将注意力转向了一类具有广义指数内核的多元标记鹰派过程，其中包括所谓的Erlang内核。我们在内核函数上提供明确的条件，以及原始过程的一定转换为Markovian和$ v $ - 地球上的Ergodic的标记动力学。我们最终证明后一个结果本身就是感兴趣的，它构成了一个关键要素，即表明总体指数霍克斯的过程属于准类样品分析的应用范围。
We develop a quasi-likelihood analysis procedure for a general class of multivariate marked point processes. As a by-product of the general method, we establish under stability and ergodicity conditions the local asymptotic normality of the quasi-log likelihood, along with the convergence of moments of quasi-likelihood and quasi-Bayesian estimators. To illustrate the general approach, we then turn our attention to a class of multivariate marked Hawkes processes with generalized exponential kernels, comprising among others the so-called Erlang kernels. We provide explicit conditions on the kernel functions and the mark dynamics under which a certain transformation of the original process is Markovian and $V$-geometrically ergodic. We finally prove that the latter result, which is of interest in its own right, constitutes the key ingredient to show that the generalized exponential Hawkes process falls under the scope of application of the quasi-likelihood analysis.
