  In this paper, we examine dynamic properties of particle flows for a recently
derived parameterized family of stochastic particle flow filters for nonlinear
filtering and Bayesian inference. In particular, we establish that particles
maintain desired posterior distribution without the Gaussian assumption on
measurement likelihood. Adopting the concept of Lyapunov stability, we further
show that particles stay close but do not converge to the maximum likelihood
estimate of the posterior distribution. The results demonstrate that stability
of particle flows is maintained for this family of stochastic particle flow
filters.
