We prove that bootstrap type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is ...

We present a new method for the determination of the magnetic moment distribution ρ(μ) of ferrofluid particles from the magnetization curve measured on diluted ferrofluid samples in the liquid state. The method employs the solution of the standard integral equation describing the magnetization of a non-interacting particle system in the given external field as a convolution of the Langevin func...

Using the main ideas of Tanaka, the measure-solution {Pt}t of a 3-dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven stochastic differential equation. Using this tool, the convergence to {Pt}t of solutions {P l t}t of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-Méléard is used and allow...