کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
5129632 1378639 2018 12 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise
کلمات کلیدی
60H10; 60F99; Zero-noise limit; Peano phenomenon; Growth rate of solutions to stochastic equations; Selection of a solution; Self-similar process;
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise
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 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 +∞ or −∞ as t→∞, respectively.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 132, January 2018, Pages 62-73
نویسندگان
, ,