What is meant by a linear SDE?

Question

I am sure this is a ridiculous question, but I can't seem to find a definition. I know the definition of linear ODE or PDE just by saying that the differential operator should be linear, but how does one define a linear SDE?

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Is the following correct? The SDE (driven by Brownian motion) $$dX_t=\mu(t,X_t)\mathrm{d}t+\sigma(t,X_t)\mathrm{d}B_t$$

is called linear if for all $t$, $x\mapsto \mu(t,x)$ and $x\mapsto\sigma(t,x)$ are linear functions.

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And I assume we can extend this definition to path-dependent coefficients?

Answer 1

$dX_t=(a(t)X_t+b(t))dt+(c(t)X(t)+d(t))dW_t$