Evaluating an ItoProcesss function

Question

The following is my Stochastic D.E.:

proc = ItoProcess[{\[DifferentialD]n[t] == 
    sigma*Sqrt[(2*Um)/(Pi*L)]*\[DifferentialD]w[
        t] - (\[DifferentialD]t*(Um*n[t]))/L}, n[t], {n, 1}, t, 
     Distributed[w, WienerProcess[]]]

I would like to find the value of n[0.1]. Can someone kindly guide me as to how I can do so?

Thanks!

Answer 1

According to the documentation, it seems you just need to give values to L and Um (here 1)

proc = ItoProcess[{\[DifferentialD]n[t] == 
Sqrt[(2)/(Pi)]*\[DifferentialD]w[t] - (\[DifferentialD]t*(n[t]))},
n[t], {n, 1}, t, Distributed[w, WienerProcess[]]];

now you can evaluate it

 f=RandomFunction[proc, {0., 5., 0.01}];

And visualize it

 ListLinePlot[f, Filling -> Axis]

If you want only the value at 0.01

f = RandomFunction[proc, {0., 0.01, 0.01}];  f // Normal // Last // Last // Last