Large Deviations for SDE driven by Heavy-tailed Lévy Processes

2021/01/11 by Wei Wei, Wei, Wei, Qiao Huang +3
Economics, Econometrics and Finance · Social Sciences · #60F10 #60H10 #60J76 #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2101.03856

openalex publication_date 2021/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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