Abstract
In this chapter, we analyze thegrowth of the Brownian paths\(t\mapsto B_t\) as\(t\rightarrow \infty \).
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Notes
- 1.
The calculation of the modulus of continuity for Brownian motion is due to Lévy, P. (1937). However this exercise follows Pinsky, M. (1999): Brownian continuity modulus via series expansions,J. Theor. Probab.14 (1), 261–266.
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Authors and Affiliations
Department of Mathematics, University of Arizona, Tucson, AZ, USA
Rabi Bhattacharya
Department of Mathematics, Oregon State Univeristy, Corvallis, OR, USA
Edward C. Waymire
- Rabi Bhattacharya
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- Edward C. Waymire
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Correspondence toRabi Bhattacharya.
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Bhattacharya, R., Waymire, E.C. (2016). Brownian Motion: The LIL and Some Fine-Scale Properties. In: A Basic Course in Probability Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-47974-3_10
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