dynamical system, variable in probability distribution

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I'm not mathematician... I have a question:

If I have a variable $n$ that can evolve in time. This variable have a probability distribution $D$.

Is there a mathematical "tool" that permit to obtain the expression a differential equation such as for any type of distribution $D$:

$\frac{dn}{dt} = f(D,n)$

EDIT : If I do something like : $\frac{dn}{dt} = \tau (D-n)$ does it mean that $n$ will follow $D$ at the velocity $\tau$ ?