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I have defined an Ito Process such that:

SeedRandom[1234];
proc = ItoProcess[{\[DifferentialD]X[t] == (w + k*Sin[Y[t] - X[t]])*\[DifferentialD]t + s*\[DifferentialD]W[t],
                   \[DifferentialD]Y[t] == (w + k*Sin[X[t] - Y[t]])*\[DifferentialD]t + s*\[DifferentialD]W[t]},
                  {X[t], Y[t]}, {{X, Y}, {X0, Y0}},
                  t, W \[Distributed] WienerProcess[]];
proc1 = proc /. {X0 -> 1, Y0 -> 0, k -> 1, w -> 1, s -> 0.01};
sample = RandomFunction[proc1, {0, 100, 0.01}]

and I would like to study the difference and ratios between the variables X and Y. I have spent some time searching through the RandomFunction documentation and resulting sample variable, however I haven't been able to find how to isolate a single variable. I can plot both at the same time using

ListLinePlot[sample]

but not just X or Y. It seems as though sample[[2]] is where the data is stored, but the format and how to isolate it is unclear to me even after spending time with the documentation.

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    $\begingroup$ Does sample["PathComponents"] do what you want? $\endgroup$ Commented Jul 18, 2022 at 17:07
  • $\begingroup$ @J.M. That is exactly what I am looking for! Thank you so much for your clarifying edits and answer :) $\endgroup$
    – Cameron F.
    Commented Jul 18, 2022 at 17:09

1 Answer 1

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As J.M. stated in the comments, sample["PathComponents"] allows me to isolate the variables.

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