If we have a set of experimental data: $$X=\{x_1,x_2,\ldots,x_N\}$$ is it possible to write down an equation of the kind: $$dx(t)=b(x(t))\,dt+\sigma(x(t))\,dB(t)$$ describing the process from which the data arise, in which $B(t)$ is a Brownian process, $b$ is a function of only $x(t)$ and $\sigma$ the standard deviation? In which cases is it impossible?
Thanks.