arXiv 1002.07802010-02math.PR

Fractional Lévy processes as a result of compact interval integral transformation

Heikki Tikanmäki, Yuliya Mishura

备注：: New main result
发表信息：: Stochastic Analysis and Applications, 29:6, 1081-1101, (2011)

英文摘要：

Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional Lévy processes are defined by integrating the infinite interval kernel w.r.t. a general Lévy process. In this article we define fractional Lévy processes using the compact interval representation. We prove that the fractional Lévy processes presented via different integral transformations have the same finite dimensional distributions if and only if they are fractional Brownian motions. Also, we present relations between different fractional Lévy processes and analyze the properties of such processes. A financial example is introduced as well.

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