def EulerMaruyama(xstart, ystart, xfinish, nsteps, f1, f2):
sol = [ystart]
xvals = [xstart]
h = N((xfinish-xstart)/nsteps)
for step in range(nsteps):
sol.append(sol[-1] + h*f1(sol[-1]) + h^(.5)*f2(sol[-1])*normalvariate(0,1))
xvals.append(xvals[-1] + h)
return zip(xvals,sol)
out = Graphics()
save(out,'temp')
@interact
def EulerMaruyamaExample(mu = slider(srange(0,10,.1),default=2.0), sigma = slider(srange(0,10,.1),default=0.5), plots_at_a_time = slider(range(1,100),default=10), number_of_steps = slider(range(1,1000),default=100), clear_plot = checkbox(True), auto_update=False):
html('<center>Example of the Euler-Maruyama method applied to<br>the stochastic differential equation for geometric Brownian motion</center>')
html('<center>$S = S_0 + \int_0^t \mu S dt + \int_0^t \sigma S dW$</center>')
emplot = list_plot(EulerMaruyama(0,1,1,number_of_steps,lambda x: mu*x,lambda x:sigma*x),plotjoined=True)
for i in range(1,plots_at_a_time):
emplot = emplot + list_plot(EulerMaruyama(0,1,1,100,lambda x: mu*x,lambda x:sigma*x),plotjoined=True)
if clear_plot:
out = emplot
save(out,'temp')
else:
out = load('temp')
out = out + emplot
save(out,'temp')
show(out, figsize = [8,5])
