Articlegreen2018

Path stability of stochastic differential equations driven by time-changed Lévy noises

31 citations0/0 files storedLatin American Journal of Probability and Mathematical Statistics

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed Lévy 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.

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References

1976Option pricing when underlying stock returns are discontinuous 2008Stochastic differential equations and applications 2004Lévy Processes and Stochastic Calculus 2009Lévy Processes and Stochastic Calculus 1989Theory of Martingales 2010Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations

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