On shot noise processes attracted to fractional Lévy motion
Convergence in distribution of an integrated shot noise process to α-stable fractional Lévy motion (1 < α < 2) is discussed. We show also that the class of limiting processes contains some non-stable self-similar processes.
KeywordsShot Noise Noise Process Fractional Brownian Motion Poisson Point Process Lebesgue Dominate Convergence Theorem
Unable to display preview. Download preview PDF.
- F. Avram, M.S. Taqqu, Weak convergence of moving averages with infinite variance, in Dependence in Probability and Statistics, pp. 319–415, Birkhäuser, 1986.Google Scholar
- L. Giraitis, D. Surgailis, On Shot Noise Processes with Long Range Dependence, Preprint.Google Scholar
- G. Samorodnitsky, M.S. Taqqu, The Various Linear Fractional Lévy Motions, in Probability, Statistics and Mathematics: Papers in Honor of Samuel Karlin, pp. 261–270, Academic Press, 1989.Google Scholar