Persistence probabilities via large deviations

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。

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.