Remark on pathwise uniqueness of stochastic differential equations driven by Lévy processes. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Takeuchi, Atsushi; Tsukada, Hiroshi
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 2(2019)
• Page Start: 155
• Page End: 170
• Publication Date: 2019-03-04
• Subjects: Pathwise uniqueness -- stochastic differential equations -- Lévy processes; 60H10 -- 60G51 -- 60H30 -- 60J75; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2018.1541750
• Languages: English
• ISSNs: 0736-2994

Abstract

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.