I want to run an Ito stochastic Process.
with the following:
b1b = 0.9; b3b = .8; a1b = 0.1; a3b = 0.2; eps = 0.1; G = (1/eps^2)*b1b ; a1 = (1/eps^2)*a1b; a3 = (1/eps^2)*a3b; xc = Sqrt[a1/a3]; Uc = a1*xc^2/2 - a3*xc^4/4
And I want to stop the process when
U[x[t]]=U[xc] and y[t]=0 (or at least very close for each of these parameters: say in the vicinity of
10^-4*U[xc] for U[x[t]] and10^-8 for y[t]
). Please noteU[x]` is the integral of U'[x].
I am trying to write a code that simulates
dz[t] for many realisations (say 100) and calculates the average of times at which the aforementioned constraint is satisfied (i.e., average of 100 times). However, I have no idea how to incorporate the contsraints and extract the time at which the contraints are satisfied.
I tried to use the
ItoProcess function, but had no fruitful outcome. Any help would be much appreciated.