标题： 一阶强逼近标量 SDE，值在一个域内 显示英文标题

标题： First order strong approximations of scalar SDEs with values in a domain

摘要： 我们关注的是强逼近一维随机微分方程（SDE），这些方程具有非Lipschitz系数且取值于某个域。 在一组一般性假设下，我们推导出一种保持SDE域的隐式格式，并且以速率一强收敛。 此外，我们证明了这个一般性结果可以应用于我们在数理金融和生物数学中遇到的许多SDE。 我们将通过分析经典的一维SDE（子线性系数：CIR模型、CEV模型和Wright-Fisher扩散；超线性系数：3/2波动率、Ait-Sahalia模型）来展示我们的方法的灵活性。 我们的目标是为一类丰富的SDE族证明一种有效的多层Monte Carlo (MLMC) 方法的有效性，这依赖于良好的强收敛性质。 显示英文摘要

摘要： We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general result can be applied to many SDEs we encounter in mathematical finance and bio-mathematics. We will demonstrate flexibility of our approach by analysing classical examples of SDEs with sublinear coefficients (CIR, CEV models and Wright-Fisher diffusion) and also with superlinear coefficients (3/2-volatility, Ait-Sahalia model). Our goal is to justify an efficient Multi-Level Monte Carlo (MLMC) method for a rich family of SDEs, which relies on good strong convergence properties.