Persistence probabilities via large deviations

持久性涉及随机过程具有异常长的偏移的概率问题。这种概率的衰减率由持续指数决定。这类问题是概率论中的经典问题。它被认为是非常困难的;尽管最近在该领域的活动很高，但一般的方法是不可用的。拟议项目的新的攻击角度是将大偏差技术应用于持久性类型问题，以获得新的持久性指数，变分公式，或通过适当的大偏差原则持久性指数的界限。在持久性概率的背景下引入大偏差方法是新的，可以是一种有前途的方法，以了解持久性类型问题背后的一般原则。

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.