Remark on pathwise uniqueness of stochastic differential equations driven by Lévy processes. Issue 2 (4th March 2019) - Takeuchi, Atsushi; Tsukada, Hiroshi
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.