An explicit solution to the Skorokhod embedding problem for double exponential increments

Abstract

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, 1971) and improves their rate of strong convergence (Gorostiza and Griego, 1980). We finalize by providing an extension regarding the embedding of a random walk with asymmetric double exponential increments.