We show that the addition of a suitable Stratonovich noise prevents the explosion for ODEs with drifts of super-linear growth, in dimension d≥2. We also show the existence of an invariant measure and the geometric ergodicity for the corresponding SDE.
Non-explosion by Stratonovich noise for ODEs / M. Maurelli. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 25(2020), pp. 68.1-68.10. [10.1214/20-ECP347]
Non-explosion by Stratonovich noise for ODEs
M. Maurelli
2020
Abstract
We show that the addition of a suitable Stratonovich noise prevents the explosion for ODEs with drifts of super-linear growth, in dimension d≥2. We also show the existence of an invariant measure and the geometric ergodicity for the corresponding SDE.
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