Spectral analysis of the zigzag process
Abstract
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$spectrum for the generator of the onedimensional zigzag process is obtained in the case where the marginal stationary distribution on $\mathbb R$ is unimodal and the refreshment intensity is zero. Sufficient conditions are obtained for a spectral mapping theorem, mapping the spectrum of the generator to the spectrum of the corresponding Markov semigroup. Furthermore results are obtained for symmetric stationary distributions and for perturbations of the spectrum, in particular for the case of a nonzero refreshment intensity.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.01691
 Bibcode:
 2019arXiv190501691B
 Keywords:

 Mathematics  Probability;
 Mathematics  Spectral Theory;
 37A30;
 65C05;
 47D07
 EPrint:
 39 pages, 1 figure