论文标题
订单K及以后的分数泊松过程
Fractional Poisson Processes of Order k and Beyond
论文作者
论文摘要
在本文中，我们在n维欧几里得空间中介绍了订单k的分数泊松长石$ r_n^+$。我们还在订单K的时间分数泊松过程，订单k的空间式泊松过程以及阶段分数泊松过程的回火版本在一维欧几里得空间中$ r_1^+$。这些过程是根据分数复合泊松过程定义的。订单k的时间折叠泊松过程自然将泊松过程和托有泊松过程概述为重量的等待时间计数过程。订单K的空间分数泊松过程允许在任何间隔中平均无限的到达数量。我们得出边缘概率，管理引入过程的差异方程。我们还为渡边的马丁纳尔（Martingale）进行了一些变化的泊松过程。
In this article, we introduce fractional Poisson felds of order k in n-dimensional Euclidean space $R_n^+$. We also work on time-fractional Poisson process of order k, space-fractional Poisson process of order k and tempered version of time-space fractional Poisson process of order k in one dimensional Euclidean space $R_1^+$. These processes are defined in terms of fractional compound Poisson processes. Time-fractional Poisson process of order k naturally generalizes the Poisson process and Poisson process of order k to a heavy tailed waiting times counting process. The space-fractional Poisson process of order k, allows on average infinite number of arrivals in any interval. We derive the marginal probabilities, governing difference-differential equations of the introduced processes. We also provide Watanabe martingale characterization for some time-changed Poisson processes.
