Strong invariance and noise-comparison principles for some parabolic stochastic PDEs

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2014-04-28 DOI:10.1214/15-AOP1009

Mathew Joseph, D. Khoshnevisan, C. Mueller

引用次数: 15

Abstract

We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.

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一些抛物型随机偏微分方程的强不变性和噪声比较原理

我们考虑一个整数格上的相互作用扩散系统。通过让网格尺寸趋近于零并使用合适的缩放，我们表明系统(在强意义上)收敛于实线上随机热方程的解。得到了不同非线性随机热方程积矩的比较不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.