A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian setting. We obtain bounds for the asymptotic rate of the expected square error of…

For $0<\alpha\leq 2$ and $0<\beta\leq 1$ let $X$ be the $(d,\alpha,\beta)$-superprocess, i.e. the superprocess with $\alpha$-stable spatial movement in $R^d$ and $(1+\beta)$-stable branching. Given that the initial measure $X_0$ is Lebesgue on $R^d$, Iscoe conjectured in [7] that the total…