  The diffusive dynamics of a particle in a medium with space-dependent
friction coefficient is studied within the framework of the inertial Langevin
equation. In this description, the ambiguous interpretation of the stochastic
integral, known as the It\^{o}-Stratonovich dilemma, is avoided since all
interpretations converge to the same solution in the limit of small time steps.
We use a newly developed method for Langevin simulations to measure the
probability distribution of a particle diffusing in a flat potential. Our
results reveal that both the It\^{o} and Stratonovich interpretations converge
very slowly to the uniform equilibrium distribution for vanishing time step
sizes. Three other conventions exhibit significantly improved accuracy: (i) the
"isothermal" (H\"{a}nggi) convention, (ii) the Stratonovich convention
corrected by a drift term, and (iii) a new convention employing two different
effective friction coefficients representing two different averages of the
friction function during the time step. We argue that the most physically
accurate dynamical description is provided by the third convention, in which
the particle experiences a drift originating from the dissipation instead of
the fluctuation term. This feature is directly related to the fact that the
drift is a result of an inertial effect that cannot be well understood in the
Brownian, overdamped limit of the Langevin equation.
