Modelling and simulating systems with state-dependent diffusion
We propose a framework for modelling stochastic systems with
state-dependent diffusion coefficients. Rather than specifying the
dynamics through a state-dependent drift and diffusion coefficients,
assuming detailed balance we specify an equilibrium probability
density and a state-dependent diffusion coefficient. We argue that
our framework is more natural from the modelling point of view and has
a distinct advantage in situations where either the equilibrium
probability density or the diffusion coefficient is discontinuous. We
introduce a numerical method for simulating dynamics in our framework
that samples from the equilibrium probability density exactly and
elegantly handles discontinuities in the coefficients. This is joint
work with Xin Yang.