  We consider a thermal particle which is diffusing in velocity-space and in a
weakly confining potential characterized by the inverse hyperbolic sine
function of the particle velocity $v$ and the control parameter $v_c$. The
stationary state of the Fokker-Planck equation is shown to be a canonical
probability distribution. Furthermore an appropriate re-parametrization relates
this stationary state with the $\kappa$-deformed Gaussian.
