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I have an SDE system which I solve using

proc = ItoProcess[{\[DifferentialD]kai1[z] == 
    0.0001*I*kai1[z] \[DifferentialD]w1[z] + 
     I*kai1 [z] \[DifferentialD]w2[z] - 
     I*kai3[z] \[DifferentialD]w3[z] + kai3[z] \[DifferentialD]w4[z] +
      kai1[z] \[DifferentialD]z,
   \[DifferentialD]kai2[z] == 
    I*kai2[z] \[DifferentialD]w1[z] + .1*I*
      kai2[z] \[DifferentialD]w2[z] - 
     I*kai4[z] \[DifferentialD]w3[z] + kai4[z] \[DifferentialD]w4[z] +
      kai2[z] \[DifferentialD]z,
   \[DifferentialD]kai3[z] == 
    I*kai1[z] \[DifferentialD]w1[z] - 
     I*kai3[z] \[DifferentialD]w2[z] + 
     I*kai1[z] \[DifferentialD]w3[z] + kai1[z] \[DifferentialD]w4[z] +
      kai3[z] \[DifferentialD]z,
   \[DifferentialD]kai4[z] == 
    I*kai4[z] \[DifferentialD]w1[z] + 
     I*kai1[z] \[DifferentialD]w2[z] - 
     I*kai3[z] \[DifferentialD]w3[z] + kai3[z] \[DifferentialD]w4[z] +
      kai1[z] \[DifferentialD]z}, {kai1[z], kai2[z], kai3[z], 
   kai4[z]}, {{kai1, kai2, kai3, kai4}, {1, 0, 0, 1}}, 
  z, {w1 \[Distributed] WienerProcess[], 
   w2 \[Distributed] WienerProcess[], 
   w3 \[Distributed] WienerProcess[], 
   w4 \[Distributed] WienerProcess[]}]

and then

sol = RandomFunction[proc, {0, 1, 0.01}]

I can then plot the solution via

ListLinePlot[Abs[sol]^2 , PlotRange -> All]

But how can I extract just one of the solutions, ie kai1,2,3,4?

Thanks

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Given sol from your code, I'd do it like this:

data = sol["Path"];
munger[{x_, y_}] := {x, Abs[#]^2} & /@ y
{path1, path2, path3, path4} = Transpose[munger /@ data];
ListLinePlot[{path1, path2, path3, path4}, PlotLegends -> {kai1, kai2, kai3, kai4}]

plot

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sol is TemporalData so you can extract the data from it

abs = Abs[sol]^2;
data = abs["Paths"][[1, 2 ;;]];
split = Table[{#[[1]], #[[2, i]]} & /@ data, {i, 1, 4}];

split has 4 elements corresponding to the x, y values for each function.

ListLinePlot /@ split // GraphicsRow

enter image description here

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