We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own techniques. It is part of the family of the so-called $\varepsilon$-strong approximations. More precisely, our approach constructs jointly the sequences of exit times and corresponding exit positions of some well-chosen domains, the construction of these domains being an important step. Based on this procedure, we emphasize an algorithm which is easy to implement. Moreover, we can develop the method for any dimension. We treat separately the integer dimension case and the non integer framework, each situation requiring appropriate techniques. In particular, for both situations, we show the convergence of the scheme and provide the control of the efficiency with respect to the small parameter $\varepsilon$. We expand the theoretical part by a series of numerical developments.

翻译：我们考虑贝塞尔进程的路径近似,并开发出一个新的高效算法。 这项研究基于作者最近的工作, 布朗运动的路径近似, 以及特定技术的构建。 它是所谓的瓦列普西隆元强近似家族的一部分。 更准确地说, 我们的方法是联合构建退出时间的序列和一些选择良好的域的相应退出位置, 这些领域的构建是一个重要步骤。 基于此程序, 我们强调一个易于执行的算法。 此外, 我们可以为任何维度制定方法。 我们分别处理整数维量案例和非整数框架, 每一种情况都需要适当的技术。 特别是, 对于这两种情况, 我们展示了计划的统一性, 并提供了对小参数 $ 瓦列普西隆元效率的控制。 我们通过一系列数字发展来扩展理论部分 。