I'm trying to explain the fact that a Brownian motion has independent increments by highlighting disjoint segments of a sample path of a Brownian motion. So, given a sample path of a (standard) Brownian motion

ListLinePlot[RandomFunction[WienerProcess[], {0, 1, 0.01}]]

how does one color the trajectory (for example) from 0.1 to 0.3 red, and from 0.5 to 0.8 blue?

ListLinePlot[RandomFunction[WienerProcess[], {0, 1, 0.01}],
     Mesh -> {{0.1,0.3,0.5,0.8}}, 
     MeshFunctions -> {#1 &},
     MeshShading -> {Black,Red, Black,Blue}]

enter image description here

  • $\begingroup$ This is exactly what I was looking for. Thanks very much! $\endgroup$ – Peter Jun 29 '17 at 17:07

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