Wiener Process Sampling

[diffeqslvr]

As a sanity check, I try to simulate a pure Wiener process du = D dW. However, when I plot the variable, it does not look like a random walk; rather, the curves follows line segments:

Is that because I am doing something wrong or because the Wiener process is not sampled at every time step since it is scale invariant? If so, how does the solver decide when to sample?

My code:

import StochasticDiffEq as SDE
D = 1
u₀ = 0
f(u, p, t) = 0
g(u, p, t) = D
tspan = (0.0, 10.0)
prob = SDE.SDEProblem(f, g, u₀, tspan)

sol = SDE.solve(prob, SDE.SRIW1(), abstol = 1e-3, reltol = 1e-3, saveat = 1e-4);

[drandran12]

I remember hitting this once too. I think it is indeed the adaptive stepsize controllor. Can you try using a fixed stepsize using dt kwarg.