论文标题
随机和非随机积分器的漂移涉及随时间变化的随机微分方程的强近似
Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators
论文作者
论文摘要
研究了一类随机微分方程（SDE）的各种近似方案的强收敛速率，该方程涉及逆下属的随机时间变化。要考虑的SDE在两个不同的方面是唯一的：i）它们包含两个漂移术语，一个是由随机时间变化驱动的，另一个是由常规，非随机时间变量驱动的； ii）标准Lipschitz的假设被随着时变的Lipschitz结合所取代。第一个方面施加的困难是通过一种与基于所谓二元性原理的知名方法显着不同的方法来克服的。另一方面，第二个方面要求建立一个标准，以实现随机时间变化的指数矩。
The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique in two different aspects: i) they contain two drift terms, one driven by the random time change and the other driven by a regular, non-random time variable; ii) the standard Lipschitz assumption is replaced by that with a time-varying Lipschitz bound. The difficulty imposed by the first aspect is overcome via an approach that is significantly different from a well-known method based on the so-called duality principle. On the other hand, the second aspect requires the establishment of a criterion for the existence of exponential moments of functions of the random time change.
