Unique strong solutions of Lévy processes driven stochastic differential equations with discontinuous coefficients

ABSTRACT

We study the strong solutions for a class of one-dimensional stochastic differential equations driven by a Brownian motion and a pure jump Lévy process. Under fairly general conditions on the coefficients, we prove the pathwise uniqueness by showing the weak uniqueness and applying a local time technique.

KEYWORDS:

• Stochastic differential equation
• time change
• weak uniqueness
• pathwise uniqueness
• Lévy processes
• local time

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

JX's research is supported by Southern University of Science and Technology Start up fund [grant number Y01286220] and National Science Foundation of China [grant numbers 61873325 and 11831010], JZ's research is supported by Macao Science and Technology Development Fund [grant number FDCT 025/2016/A1] and Natural Sciences and Engineering Research Council of Canada (NSERC) [grant number 249554-2011] and and XZ's research is supported by NSERC [grant number RGPIN-2016-06704].