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On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise

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 نشر من قبل Andrey Pilipenko
 تاريخ النشر 2016
  مجال البحث
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We study the limit behavior of differential equations with non-Lipschitz coefficients that are perturbed by a small self-similar noise. It is proved that the limiting process is equal to the maximal solution or minimal solution with certain probabilities $p_+$ and $p_-=1-p_+$, respectively. We propose a space-time transformation that reduces the investigation of the original problem to the study of the exact growth rate of a solution to a certain SDE with self-similar noise. This problem is interesting in itself. Moreover, the probabilities $p_+$ and $p_-$ coincide with probabilities that the solution of the transformed equation converges to $+infty$ or $-infty$ as $ttoinfty,$ respectively.



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