Remark on pathwise uniqueness of stochastic differential equations driven by Lévy processes

Abstract

Consider real-valued processes determined by stochastic differential equations driven by Lévy processes. The jump parts of the driving Lévy process are not always α-stable ones, nor symmetric ones. In the present article, we shall study the pathwise uniqueness of the solutions to the stochastic differential equations under the conditions on the coefficients that the diffusion and the jump terms are Hölder continuous, while the drift one is monotonic. Our approach is based on Gronwall’s inequality.

Keywords:

• Pathwise uniqueness
• stochastic differential equations
• Lévy processes

2010 Mathematics Subject Classifications:

• 60H10
• 60G51
• 60H30
• 60J75

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author was supported by JSPS-MAEDI Sakura program.