EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

Author:

SCHEUTZOW MICHAEL1

Affiliation:

1. Institut für Mathematik, MA 7-5, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany

Abstract

In this survey, we provide some tools to obtain estimates for the almost sure exponential growth rate of a stochastic delay differential equation (sdde) which fixes zero. In particular, we are interested in determining whether the solutions of a given sdde are exponentially stable (i.e. have a negative exponential growth rate) or not. We focus on equations without drift, which are a good testground to assess if a method is powerful enough to discriminate between stability and instability when a certain parameter (e.g. noise intensity) varies. The most powerful tool we provide is the method of Lyapunov functionals which is used to obtain upper bounds for p-th moment exponents for small (positive and negative) values of p.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3