Hi all,

I am trying to fit the following matrix SDE using the following code:

```
G = [0 -1; 1 0];
p = (A=G, B=G)
function drift(du, u, p, t) ## drift function for the SDE
du = t * p.A;
end # drift
function diffusion(du, u, p, t) ## diffusion function for the SDE
du = t * p.B;
end
time_tot = 1.0;
tspan = (0.0, time_tot);
u0 = reshape(zeros(4), (2,2))
prob = SDEProblem(drift, diffusion, u0, tspan, p=p); ## setup SDE problem
sol = solve(prob, EM(), p=p, dt=0.001); ## Solve using E-M scheme NOT WORKING!
```

This doesn’t work at all. No errors are thrown but the solution never moves from its initial condition u0. Can someone please tell me how to correctly code this matrix SDE, or suggest some reading material for me. Is a mass matrix required? If so, what would it look like and how do I include it in the problem formulation?

Thanks,

Simone.

Edit: What I really want is to constrain the solution to be skew-symmetric. How do I do that? The following code works but the solutions are not skew-symmetric. I guess you need the mass matrix to provide the constraints? If so, how?

```
G = [0 -1; 1 0];
p = (A=G, B=G);
function drift(du, u, p, t) ## drift function for the SDE
du[1] = t * p.A[1,1];
du[2] = t * p.A[1,2];
du[3] = t * p.A[2,1];
du[4] = t * p.A[2,2];
end # drift
function diffusion(du, u, p, t) ## diffusion function for the SDE
du[1] = t * p.B[1,1];
du[2] = t * p.B[1,2];
du[3] = t * p.B[2,1];
du[4] = t * p.B[2,2];
end
time_tot = 1.0;
tspan = (0.0, time_tot);
u0 = reshape(zeros(4), (2,2));
prob = SDEProblem(drift, diffusion, u0, tspan, p=p); ## setup SDE problem
sol = solve(prob, p=p, dt=0.001);
sol.u
```