Hölder continuity of semigroups for time changed symmetric stable processes

doi:10.1007/s11464-015-0501-z

Front. Math. China

2016, Vol. 11

Issue (1) : 109-121 https://doi.org/10.1007/s11464-015-0501-z

research-article

Hölder continuity of semigroups for time changed symmetric stable processes

Dejun LUO¹,Jian WANG^2,^*(

)

1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100190, China
2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007,China

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Abstract

Let(Zt)t≥0be a one-dimensional symmetric α-stable process withα∈(0,2), and letσbe a bounded (from above and from below) and 1/(α∨1)-Hölder continuous function on?. Consider the stochastic differential equationdX=σ(Xt−)dZt,which admits a unique strong solution. By using thesplitting technique and the coupling method, we derive the Hölder continuity of the associated semigroup.

Keywords Symmetric stable process time-change Hölder continuity coupling

Corresponding Author(s): Jian WANG

Issue Date: 02 December 2015

Cite this article:

Dejun LUO,Jian WANG. Hölder continuity of semigroups for time changed symmetric stable processes[J]. Front. Math. China, 2016, 11(1): 109-121.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0501-z
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/109

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