论文标题
在马尔可夫添加剂过程和马尔可夫调制广义的Ornstein-uhlenbeck过程方面
On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein-Uhlenbeck processes
论文作者
论文摘要
我们为存在建立了足够的条件，并为$κ$'Th Moments，$κ\ geq 1 $提供了明确的公式，Markov调制了广义的Ornstein-Uhlenbeck过程及其固定分布。特别是，根据驾驶马尔可夫添加剂的特征，得出了固定分布的运行均值，自动助力函数和整数矩。我们的派生依赖于马尔可夫添加过程的矩和（多维）积分的新一般结果。
We establish sufficient conditions for the existence, and derive explicit formulas for the $κ$'th moments, $κ\geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In particular, the running mean, the autocovariance function, and integer moments of the stationary distribution are derived in terms of the characteristics of the driving Markov additive process. Our derivations rely on new general results on moments of Markov additive processes and (multidimensional) integrals with respect to Markov additive processes.
