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RESEARCH PRODUCT

First hitting time for a diffusion

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In this thesis, we focus our attention on the generation of the first exit time or the first passage time for diffusions in a one-dimensional context.In the first chapter, we present already well-known methods in order to generate such random variables. We particularly introduce the WOMS algorithm. This algorithm permits the generation of an approximation of the time needed by the Brownian motion in order to exit from a given interval.In the second and third chapters, we explain how to extend the previous algorithm in order to deal with diffusions strongly linked to the one-dimensional Brownian motion. We first consider the Ornstein-Uhlenbeck process, and then we consider a wide class of diffusions called the L-class diffusions.In the fourth and last chapter, we study the generation of the first passage time through a given level for jump diffusions. This part of the study is based on the so-called exact simulation methods and also on the famous Girsanov's formula.