I am not really into solving stochastic differential equations, but I was trying to numerically solve an OED given by:
$\frac{dy}{dt} = f(t,y,p) + N(0,\sigma^2)$
where normal noise with 0 mean and given variance is added and p is a set of estimated parameters.
I have been reading sime stuff about it and I am solving it using a Euler-Maruyama approach:
$Y_{n+1} = Y_n + f(t,y,p)\cdot\Delta t + \sigma\cdot\sqrt{\Delta t}\cdot N(0,1)$
with a given time step. Is this a correct approach?
Kind regards.
Yes, it is a correct scheme for the simulation of the SDE $$ \mathrm dy_t = f(t,y_t,p)\mathrm dt+\sigma \mathrm dW_t $$ where informally $\sigma \mathrm d W_t \sim \mathcal N(0,\sigma^2\mathrm dt)$.