Particle filtering approximations for a Gaussian-generalized inverse Gaussian model

We consider the filtering problem for a class of discrete-time partially observable stochastic processes. Under strong conditions on the parameters involved and on the initial condition, we are able to prove that it admits a finite dimensional filter. Relaxing these assumptions, we use a Rao Blackwellization procedure to perform a Particle filtering approximation of the filtering distribution, then we prove its convergence and extend this study to a jump Markov model.