Abstract
Two important Markov processes derived from Brownian motion starting from a point x ≥ 0 are (i) Brownian motion absorbed at zero and (ii) Brownian motion reflected at zero. The precise definitions of these two processes are given and their structure delineated, including the Markov property and the computation of the transition probabilities.
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Bhattacharya, R., Waymire, E.C. (2021). Brownian Motion on the Half-Line: Absorption and Reflection. In: Random Walk, Brownian Motion, and Martingales. Graduate Texts in Mathematics, vol 292. Springer, Cham. https://doi.org/10.1007/978-3-030-78939-8_19
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DOI: https://doi.org/10.1007/978-3-030-78939-8_19
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78937-4
Online ISBN: 978-3-030-78939-8
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