کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5129632 | 1489847 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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 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 pâ coincide with probabilities that the solution of the transformed equation converges to +â or ââ as tââ, respectively.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 132, January 2018, Pages 62-73
Journal: Statistics & Probability Letters - Volume 132, January 2018, Pages 62-73
نویسندگان
Andrey Pilipenko, Frank Norbert Proske,