空间中具有粗糙噪声和粗糙初始条件的抛物型Anderson模型

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-01-01 DOI:10.1214/22-ecp506

R. Balan, Le Chen, Yiping Ma

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引用次数: 1

摘要

在本文中，我们考虑了R+×R上的抛物型Anderson模型，该模型由高斯噪声驱动，高斯噪声在时间上是分数的，索引为H0>1/2，在空间上是分数，索引为03/4。在初始数据的一般条件下，我们证明了温和解的存在性和唯一性，并得到了p≥2的所有p阶矩在时间上的指数上界。

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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Parabolic Anderson model with rough noise in space and rough initial conditions

In this note, we consider the parabolic Anderson model on R + × R , driven by a Gaussian noise which is fractional in time with index H 0 > 1 / 2 and fractional in space with index 0 < H < 1 / 2 such that H 0 + H > 3 / 4. Under a general condition on the initial data, we prove the existence and uniqueness of the mild solution and obtain its exponential upper bounds in time for all p -th moments with p ≥ 2.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.