Definition of a diffusion coefficient

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Main Question or Discussion Point

Consider this Ito proces: $$dX_t = \mu(X_t,t)dt+\sigma(X_t,t)dW_t$$ with W_t being a wiener process. My question: What is the diffusion coefficient of X?

My motivation for asking: A lot if financial literature refer to "diffusion coefficient" and I haven't understood by googling it, because most google hits take me to a site where the diffusion coefficient is defined within some specific problem in physics.
 

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