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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability of the solution of stochastic differential equation driven by time-changed Lévy noise
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by Erkan Nane and Yinan Ni PDF
Proc. Amer. Math. Soc. 145 (2017), 3085-3104 Request permission

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
  • MR Author ID: 782700
  • Email: ezn0001@auburn.edu
  • Yinan Ni
  • Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
  • MR Author ID: 1160230
  • Email: yzn0005@auburn.edu
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3085-3104
  • MSC (2010): Primary 65C30
  • DOI: https://doi.org/10.1090/proc/13447
  • MathSciNet review: 3637955