稳定Lévy运动的两个多稳定扩张及其半鞅表示
On two multistable extensions of stable Lévy motion and their semimartingale representation
摘要：
我们比较了多稳定Lévy运动的两种定义。这些过程是经典Lévy运动的扩展，其中允许稳定性指数随时间变化。我们证明了两个多稳定Lévy运动具有不同的性质：特别地，一个是纯跳马尔可夫过程，而另一个不满足这些性质.我们证明了两者都是半鞅，并提供半鞅分解。
英文摘要：
We compare two definitions of multistable Lévy motions. Such processes are extensions of classical Lévy motion where the stability index is allowed to vary in time. We show that the two multistable Lévy motions have distinct properties: in particular, one is a pure-jump Markov process, while the other one satisfies neither of these properties. We prove that both are semimartingales and provide semimartingale decompositions.
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