Total approximation order for Markov jump process filtering given discretized observations

The note proceeds the investigation devoted to the numerical approximation of the Markov jump process filtering given both the counting and diffusion observations with the multiplicative noise. The filtering estimates are approximated using the observations, previously discretized by time. By contrast with the previous algorithms which limit the number of the Markov state transitions that occurred during the time discretization interval, the new estimates are free of these restrictions and constructed via a unified scheme. The note presents an upper bound for the approximation accuracy as a function of the observation system parameters, applied scheme of the numerical integration, the time discretization step, and the filtering moment. A numerical example illustrates a sublinear character of the bound towards the latter argument.