I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see https://math.stackexchange.com/questions/1385633/solving-sde-fracdytdt-c-sigma-wwtyt-epsilont. My approach is using Mathematica. However, I have not been able to specify this SDE in Mathematica. As far as I understand, the ItoProcess
function is appropriate. I have come this far:
proc =
ItoProcess[
{\[DifferentialD]y[t] == c*y[t]\[DifferentialD]t +
e[t]*\[DifferentialD]t + σ*y[t]*w[t]},
y[t], {y, y0}, t, Distributed[w, WienerProcess[]]]
How do I now tell Mathematica that e[t]
is a gaussian white noise process, c
is a scalar and σ
a non-negative scalar?
{}
button above the edit window. The edit window help button?
is also useful for learning how to format your questions and answers. You may also find this this meta Q&A helpful $\endgroup$ – Michael E2 Aug 7 '15 at 14:02