论文标题
一类半马尔科夫动力学的半明星表示
Semimartingle Representation of a class of Semi-Markov Dynamics
论文作者
论文摘要
我们考虑一类半马尔可夫过程（SMP），以便嵌入的离散时间马尔可夫链可能是非均匀的。相应的增强过程使用涉及泊松随机度量的随机积分方程表示为半明丁。建立了方程式的存在和独特性。随后，我们表明该解决方案确实是具有所需过渡速率的SMP。最后，我们得出了从具有两个不同初始条件的方程式的两个解决方案获得的双变量过程的定律。
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation involving a Poisson random measure. The existence and uniqueness of the equation are established. Subsequently, we show that the solution is indeed a SMP with desired transition rate. Finally, we derive the law of the bivariate process obtained from two solutions of the equation having two different initial conditions.
