Time Change Equations for L\'evy Type Processes
Time Change Equations for L\'evy Type Processes
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DOI：
10.1016/j.spa.2017.06.011
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
Paul Kruhner;Alexander Schnurr
中科院分区：
文献类型：
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作者：
Paul Kruhner;Alexander Schnurr
我们考虑 Lévy 型过程的时间变化方程。在这种情况下，我们概括了 Böttcher 等人的结果。 （2013）显着。也就是说，我们能够合并可测量的而不是连续的乘数。这打开了一扇门，可以找到确实存在相应过程的整个符号类别。为了建立我们的结果，我们仔细分析了时间变化方程和经典初始值问题之间的联系。这种关系使我们能够将纯数学这一经典学科的众所周知的结果转移到随机过程理论中。在证明我们的主要定理的过程中，我们在 Lévy 型过程的路径上建立了结果的概括。
We consider time change equations for Lévy-type processes. In this context we generalize the results of Böttcher et al. (2013) significantly. Namely, we are able to incorporate measurable instead of continuous multipliers. This opens a gate to find whole classes of symbols for which corresponding processes do exist. In order to establish our results we carefully analyze the connection between time change equations and classical initial value problems. This relationship allows us to transfer well-known results from this classical subject of pure mathematics into the theory of stochastic processes. On the way to prove our main theorem we establish generalizations of results on paths of Lévy-type processes.