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18.1: Standard Brownian Motion
https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/18%3A_Brownian_Motion/18.01%3A_Standard_Brownian_Motion
This is a statement of time homogeneity: the underlying dynamics (namely the jostling of the particle by the molecules of water) do not change over time, so the distribution of the displacement of the...This is a statement of time homogeneity: the underlying dynamics (namely the jostling of the particle by the molecules of water) do not change over time, so the distribution of the displacement of the particle in a time interval \( [s, t] \) depends only on the length of the time interval.

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