Hello everyone! I'd like to investigate a first passage problem with moving boundary. I'm not good in Wolfram Mathematica and I don't see how I can modify this code (from Mathematica Help, but I'm interested not only in Wiener process)
sample = Map[FirstCase[#, _?(Last[#] >= 2 &)] &,
RandomFunction[WienerProcess[1, 1], {0, 15, 0.01}, 10^4]["Paths"]];
data0 = DeleteCases[sample, {}][[All, 1]];
data = Cases[data0, _?Positive];
Show[Histogram[data, 30, "PDF"]]
I want to replace "2" in the first code line to some function f(t)f(t) and I understand I've got to calculate the boundary at times f(ti)f(ti) and then check the condition X(ti)⩾f(ti)X(ti)⩾f(ti) and if it's true, titi is a hitting time for this trajectory, but what should I do in code?
Thanks for help and I'm sorry for bad English.