Summary: We study the small
deviation problem for a class of symmetric Lévy processes,
namely, subordinated Lévy processes. Under some mild
general assumption, we give precise estimates (up to a constant
multiple in the logarithmic scale) of the small deviation
probabilities. These probabilities, also evaluated under the
conditional probability given the subordination process A, are
formulated in terms of the Laplace exponent of A. The results
are furthermore extended to processes subordinated to the
fractional Brownian motion of arbitrary Hurst index.
Keywords: Lévy process,
subordination, small deviation, fractional Brownian motion.
2000 Mathematics Subject Classification:
60G51, 60G15, 60G52.
Download: (dvi) (pdf)