|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|5129632||1378639||2018||12 صفحه PDF||ندارد||دانلود رایگان|
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 pâ=1âp+, respectively. We propose a spaceâtime 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 pâ coincide with probabilities that the solution of the transformed equation converges to +â or ââ as tââ, respectively.
Journal: Statistics & Probability Letters - Volume 132, January 2018, Pages 62-73