Persistence probabilities via large deviations

• Applicant: Professor Dr. Frank Aurzada
• Subject Area: Mathematics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 282777864

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.

• DFG Programme: Research Grants