Séminaire de Probabilités XXXVIII
Lecture Notes in Mathematics, 2005, Volume 1857/2005, 1-4, DOI: 10.1007/978-3-540-31449-3_1

Tanaka’s Construction for Random Walks and Lévy Processes

Ronald A. Doney

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Abstract

Tanakarsquos construction gives a pathwise construction of ldquorandom walk conditioned to stay positiverdquo, and has recently been used in [3] and [8] to establish other results about this process. In this note we give a simpler proof of Tanakarsquos construction using a method which also extends to the case of Lévy processes.

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