Path stability of the solution of stochastic differential equation   driven by time-changed L\'evy noises
  This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed L\'evy noise. The conditions for the solution of time-changed SDE to be path stable and exponentially path stable are given. Moreover, we reveal the important role of the time drift in determining the path stability properties of the solution. Related examples are provided. 
Erkan Nane and Yinan Ni
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