摘要
Let （Zt）t≥o be a one-dimensional symmetric α-stable process with α ∈ （0, 2）, and let a be a bounded （from above and from below） and 1/（α V 1）- Holder continuous function on R. Consider the stochastic differential equation dXt = σ（Xt-）dZt, which admits a unique strong solution. By using the splitting technique and the coupling method, we derive the HSlder continuity of the associated semigroup.
Let （Zt）t≥o be a one-dimensional symmetric α-stable process with α ∈ （0, 2）, and let a be a bounded （from above and from below） and 1/（α V 1）- Holder continuous function on R. Consider the stochastic differential equation dXt = σ（Xt-）dZt, which admits a unique strong solution. By using the splitting technique and the coupling method, we derive the HSlder continuity of the associated semigroup.
基金
The authors were indebted to the referees for their helpful comments and careful corrections. The first author＇s work was supported by the Key Laboratory of Random Complex Structures and Data Sciences, Chinese Academy of Sciences （2008DP173182）, the National Natural Science Foundation of China （Grant No. 11571347）, and Academy of Mathematics and Systems Science （Y129161ZZ1）. The second author＇s work was supported by the National Natural Science Foundation of China （Grant Nos. 11201073 and 11522106）, the National Science Foundation of Fujian Province （2015J01003）, and the Program for Nonlinear Analysis and Its Applications （IRTL1206）.
