论文标题
特定一维扩散的强近似
Strong approximation of particular one-dimensional diffusions
论文作者
论文摘要
本文开发了一种用于一维随机过程的路径近似的新技术，更确切地说，布朗运动和随机微分方程的家族与布朗运动（通常称为L和G级）息息相关。我们在这里对$ε$ -Strong近似感兴趣。我们提出了一个易于实施的过程，该程序共同构建，出口时间的序列以及一些选择域的相应退出位置。主要结果控制了覆盖固定时间间隔的步骤数和我们方案的收敛定理。我们结合了布朗出口时间的结果，该结果来自时间扩展的结构域（一维热球）和经典的更新理论。还描述了数值示例和问题，以完成理论结果。
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually known as L and G-classes). We are interested here in the $ε$-strong approximation. We propose an explicit and easy to implement procedure that constructs jointly, the sequences of exit times and corresponding exit positions of some well chosen domains. The main results control the number of steps to cover a fixed time interval and the convergence theorems for our scheme. We combine results on Brownian exit times from time-depending domains (one-dimensional heat balls) and classical renewal theory. Numerical examples and issues are also described in order to complete the theoretical results.
