Levy processes with summable Levy measures, long time behavior

Lev Sakhnovich

Levy processes with summable Levy measures, long time behavior

Probability 2014-03-24 v1 Functional Analysis Statistics Theory Statistics Theory

Authors: Lev Sakhnovich

Abstract

In our previous paper (ArXiv:1306.1492) we have proved that a representation of the infinitesimal generators $L$ for Levy processes $X_t$ can be written down in a convolution type form. For the case of non-summable Levy measures we constructed the quasi-potential operators $B$ and investigated the long time behavior of $X_t$ . In the present paper we consider Levy processes $X_t$ with summable Levy measures. In this case the form of the quasi-potential operators $B$ essentially differs from the form in the case of non-summable Levy measures. We use this new form in order to study the long time behavior of $X_t$ for the case of summable Levy measures.

Keywords

lévy processes

Cite

@article{arxiv.1403.5456,
  title  = {Levy processes with summable Levy measures, long time behavior},
  author = {Lev Sakhnovich},
  journal= {arXiv preprint arXiv:1403.5456},
  year   = {2014}
}

Comments

This paper is a further development of our previous paper (ArXiv:1306.1492), where Levy processes with non-summable Levy measures were studied. Here we study Levy processes with summable Levy measures

Levy processes with summable Levy measures, long time behavior

Abstract

Keywords

Cite

Comments

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