Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make such an embedding explicit by means of a Poissonian scheme, which both simplifies classic constructions of strong approximations of uniform transport processes (Griego et al. (1971)) and improves their rate of strong convergence (Gorostiza et al. (1980)). We finalise by providing an extension regarding the embedding of a random walk with asymmetric double exponential increments.

中文翻译：

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双指数增量的 Skorokhod 嵌入问题的显式解

标准布朗运动的均匀传输过程的强近似依赖于具有中心双指数增量的随机游走的 Skorokhod 嵌入。在这篇笔记中，我们通过泊松方案明确了这种嵌入，这既简化了均匀传输过程的强近似的经典构造（Griego 等人（1971）），又提高了它们的强收敛率（Gorostiza 等人）。 1980))。我们通过提供关于嵌入非对称双指数增量的随机游走的扩展来最终确定。