Fokker--Planck equation - naming a vector field

Question

A Fokker Planck equation for the prob. density $\rho$ may be written in the form of a continuity equation $$\frac{\partial \rho(x,t)}{\partial t} = - \nabla \cdot \left[ g(x,t) \rho(x,t) \right].$$

The term $$ \left[ g(x,t) \rho(x,t) \right] $$ is often called the probability current or the probability flux.

I was wondering whether there is a name for the term $$ g(x,t) .$$ It is a vector field, but is there some more specific or descriptive characterisation for this term?

Answer 1

It is called the drift term (here denoted as $\mu(X_t, t)$ https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation. You have written the form with zero diffusion term, more generally: $$ \frac{\partial\rho(x,t)}{\partial t} = -\nabla [g(x, t) \rho(x,t)] + \nabla [D(x,t) \nabla p(x,t)] $$ Where $D = D_{ij}$ is the diffusion tensor.