dbm = DiscreteBrownianMotion.MultiPath.ofSize(5, 1000, .001)
"""
Solve the SDE. We define the f and g functions first, then pass them to
the solver. We also use the known solution for the SDE for comparison
purposes.
"""
def f(x):
return 2 * x
def g(x):
return x
# numeric solutions
t, Xt = DiscreteBrownianMotion.sdeEM(f, g, 1, dbm)
# exact solutions
Yt = N.exp(1.5*t + dbm.Wt)
"""
Now use a different time interval for integration than for the discretized
Brownian motion. Just expand the time interval for the Brownian motion, and
repeat the integration.
"""
expandFactor = 10
dbm2 = dbm.expandInterval(expandFactor)
t2, Xt2 = DiscreteBrownianMotion.sdeEM(f, g, 1, dbm2)
"""
Take a look at the results. We'll first examine the RMS error of the numeric