Persistence probabilities via large deviations

大偏差的持续概率

• 批准号: 282777864
• 负责人: Professor Dr. Frank Aurzada
• 金额: --
• 依托单位: Arbeitsgruppe Stochastik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/282777864?language=en
• 关键词: Persistence; probabilities; via; large; deviations

Persistence concerns the question of the probability that a stochastic process has an unusually long excursion. The rate of decay of this probability is governed by a persistence exponent. This type of question is a classical question in probability theory. It is considered very hard; and despite high recent activity in the field, general methods are not available.The new angle of attack of the proposed project is in applying large deviation techniques to persistence type problems in order to obtain new persistence exponents, variational formulas, or bounds for the persistence exponents via suitable large deviation principles. The introduction of the large deviation method in the context of persistence probabilities is new and can be a promising approach in order to understand the general principles behind persistence type questions.

持久性涉及到一个随机过程有一个异常长的偏移的概率问题。该概率的衰减率由持久性指数控制。这类问题是概率论中的经典问题。它被认为是非常困难的；尽管最近该领域的活动频繁，但没有通用的方法。所提议的项目的新攻角是将大偏差技术应用于持久性类型问题，以便通过合适的大偏差原则获得新的持久性指数、变分公式或持久性指数的边界。在持久性概率上下文中引入大偏差方法是一种新的方法，对于理解持久性类型问题背后的一般原理可能是一种很有前途的方法。

项目成果

Persistence exponents via perturbation theory : autoregressive and moving average processes

通过扰动理论的持久性指数：自回归和移动平均过程

• DOI: 10.26083/tuprints-00017566
• 发表时间: 2021
• 作者: Marvin Kettner

Persistence exponents in Markov chains

马尔可夫链中的持久性指数

• DOI: 10.1214/20-aihp1114
• 发表时间: 2021
• 期刊: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 作者: Frank Aurzada;Sumit Mukherjee;Ofer Zeitouni
• 通讯作者: Ofer Zeitouni

Persistence Exponents via Perturbation Theory: AR(1)-Processes

• DOI: 10.1007/s10955-019-02384-3
• 发表时间: 2018-10
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: F. Aurzada;Marvin Kettner