Abstract
Brownian motion (BM) as a continuous-time extension to a simple symmetric random walk has been introduced in this chapter. The stationary and independent increments, normal distribution, and Markovian property have been provided as the properties of a standard Brownian motion. Brownian motion with drift, and geometric Brownian motion have also been defined as an extension to a standard Brownian motion. Some examples and problems have been provided to clarify the basic and other properties of a Brownian motion.
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Bas, E. (2019). Introduction to Brownian Motion. In: Basics of Probability and Stochastic Processes. Springer, Cham. https://doi.org/10.1007/978-3-030-32323-3_16
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DOI: https://doi.org/10.1007/978-3-030-32323-3_16
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-32323-3
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