LPTMS PhD Proposal: Extreme Value Statistics in Stochastic Processes


Satya MAJUMDAR + 33 (0)1 69 15 64 65

Grégory SCHEHR + 33 (0)1 69 15 76 41

The extreme value statistics in stochastic processes is a subject of growing interest with applications from climate science to finance. Given a stochastic time-series over a given time interval [0,t], the typical questions are: what is the statistics of the maximum (or minimum) value of the process in this time window, at what time the maximum (or the minimum) is achieved, what is the time gap between the maximum and minimum etc.? Even for simple stochastic processes such as a one dimensional Brownian motion, these questions are often nontrivial. In the thesis, these questions would be addressed for a Brownian motion to start with, and progressively other types of stochastic processes would be studied.