کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155889 | 958780 | 2012 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension](/preview/png/1155889.png)
چکیده انگلیسی
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the non-linear stochastic heat equation in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 122, Issue 1, January 2012, Pages 418–447
Journal: Stochastic Processes and their Applications - Volume 122, Issue 1, January 2012, Pages 418–447
نویسندگان
Eulalia Nualart, Lluís Quer-Sardanyons,