Large Deviations for SDE driven by Heavy-tailed Lévy Processes

Abstract

We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed Lévy processes. These heavy-tailed Lévy processes do not satisfy the exponential integrability condition, which is a common restriction on the Lévy processes in existing large deviations contents. We further prove that the solution processes satisfy a weak large deviation principle with a discrete rate function and logarithmic speed. We also show that they do not satisfy the full large deviation principle.

18 pages

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