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Not that familiar with SDE solving, but it seems odd that there this field is empty when a sparse jacobian is built for SDEs? They are there for e.g. ODEs and Nonlinear problems. And if one shouldn't do sparse Jacobians here, shouldn't;t there at least be an error/warning?
using ModelingToolkit, StochasticDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D
using Plots
@parameters σ=10.0 ρ=2.33 β=26.0
@variables x(t)=5.0 y(t)=5.0 z(t)=1.0
@brownian B
eqs = [D(x) ~ σ * (y - x) + 0.3x * B,
D(y) ~ x * (ρ - z) - y + 0.3y * B,
D(z) ~ x * y - β * z + 0.3z * B]
@mtkbuild de = System(eqs, t)
sprob = SDEProblem(de, [], 0.0, [], jac = true, sparse = true)
sprob.f.jac_prototype == nothing # true
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