کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5130065 | 1378656 | 2017 | 35 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stochastic differential equation for Brox diffusion
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
This paper studies the weak and strong solutions to the stochastic differential equation dX(t)=â12WÌ(X(t))dt+dB(t), where (B(t),tâ¥0) is a standard Brownian motion and W(x) is a two sided Brownian motion, independent of B. It is shown that the Itô-McKean representation associated with any Brownian motion (independent of W) is a weak solution to the above equation. It is also shown that there exists a unique strong solution to the equation. Itô calculus for the solution is developed. For dealing with the singularity of drift term â«0TWÌ(X(t))dt, the main idea is to use the concept of local time together with the polygonal approximation WÏ. Some new results on the local time of Brownian motion needed in our proof are established.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 127, Issue 7, July 2017, Pages 2281-2315
Journal: Stochastic Processes and their Applications - Volume 127, Issue 7, July 2017, Pages 2281-2315
نویسندگان
Yaozhong Hu, Khoa Lê, Leonid Mytnik,