随机薛定谔延迟晶格系统的不变量和大偏差原理

Zhang Chen, Xiaoxiao Sun, Bixiang Wang
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引用次数: 0

摘要

本文关注的是具有局部利普齐兹漂移项和扩散项的随机薛定谔延迟晶格系统。基于均匀估计和解段在概率上的等连续性,我们证明了解及其段过程的概率分布族的严密性,从而证明了$l^2\times L^2((-\rho,\,0);l^2)$上存在$\rho >0$的不变度量。我们还通过弱收敛法建立了小噪声解的大偏差原理。
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Invariant measures and large deviation principles for stochastic Schrödinger delay lattice systems

This paper is concerned with stochastic Schrödinger delay lattice systems with both locally Lipschitz drift and diffusion terms. Based on the uniform estimates and the equicontinuity of the segment of the solution in probability, we show the tightness of a family of probability distributions of the solution and its segment process, and hence the existence of invariant measures on $l^2\times L^2((-\rho,\,0);l^2)$ with $\rho >0$. We also establish a large deviation principle for the solutions with small noise by the weak convergence method.

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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
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