Stability theory for Gaussian rough differential equations. Part I.
Hoang Duc Luu
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Submission date: 02. Jan. 2019 (revised version: January 2019)
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We propose a quantitative direct method of proving the stability result for Gaussian rough differential equations in the sense of Gubinelli. Under the strongly dissipative assumption of the drift coefficient function, we prove that the trivial solution of the system under small noise is exponentially stable.