Adaptive timestepping for SDEs with non-globally Lipschitz drift

Thesis

In this thesis, we focus on the numerical approximation of SDEs with a drift which is not globally Lipschitz, and corresponding sensitivity calculations.

First, we propose an adaptive timestep construction for an Euler- Maruyama approximation of these SDEs over a finite time interval. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Moreover, we ex...

Expand abstract

Authors: Fang, W

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Chaotic System; Multilevel Monte Carlo; Numerical method; Adaptive; Ergodic SDE
• Subjects: Mathematics