Spectral theory for one-dimensional symmetric Levy processes killed upon hitting the origin

Details Spectral theory for one-dimensional symmetric Levy processes killed upon hitting the origin Spectral theory for one-dimensional symmetric Levy processes killed upon hitting the origin

2011-10-26

arxiv.org/abs/1110.5894v2

Mathematics

Probability

29 pages, 3 figures

Scientific paper

Spectral theory for the transition semigroup of one-dimensional symmetric Levy process killed upon hitting the origin is studied. Under very mild assumptions, an integral-type formula for eigenfunctions is obtained, and eigenfunction expansion of transition operators and the generator is given. As an application, integral fomulae for the transition density and the distribution of the hitting time of the origin are proved.

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