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Stability of the solution of stochastic differential equation driven by time-changed Lévy noise


Authors: Erkan Nane and Yinan Ni
Journal: Proc. Amer. Math. Soc. 145 (2017), 3085-3104
MSC (2010): Primary 65C30
DOI: https://doi.org/10.1090/proc/13447
Published electronically: January 27, 2017
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Abstract: This paper studies stabilities of the solution of stochastic differential equations (SDE) driven by time-changed Lévy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics, biology, engineering, finance and hydrology. Necessary conditions for the solution of time-changed SDE to be stable in different senses will be established. The connection between stability of the solution to time-changed SDE and that to corresponding original SDE will be disclosed. Examples related to different stabilities will be given. We study SDEs with time-changed Lévy noise, where the time-change processes are the inverse of general Lévy subordinators. These results are an important generalization of the results of Q. Wu (2016).


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Additional Information

Erkan Nane
Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
Email: ezn0001@auburn.edu

Yinan Ni
Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
Email: yzn0005@auburn.edu

DOI: https://doi.org/10.1090/proc/13447
Received by editor(s): April 25, 2016
Received by editor(s) in revised form: April 26, 2016, and August 23, 2016
Published electronically: January 27, 2017
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2017 American Mathematical Society