Invariant measures under random integral mappings and marginal distributions of fractional L\'evy processes

Zbigniew J. Jurek

Invariant measures under random integral mappings and marginal distributions of fractional L\'evy processes

Probability 2012-10-23 v1

Authors: Zbigniew J. Jurek

Abstract

It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of generalized s-selfdecomposable and selfdecomposable distributions. Some application are given to the moving average fractional L\'evy process (MAFLP).

Keywords

invariant measures random integral mappings infinitely divisible distributions selfdecomposable distributions fractional Lévy processes

Cite

@article{arxiv.1206.3047,
  title  = {Invariant measures under random integral mappings and marginal distributions of fractional L\'evy processes},
  author = {Zbigniew J. Jurek},
  journal= {arXiv preprint arXiv:1206.3047},
  year   = {2012}
}

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