Robust filtering algorithm for Markov jump processes with high-frequency counting observations

We present an algorithm for estimating the state ofMarkov jump processes, given the counting observations. A characteristic feature of the class of considered observation systems is that the frequency of jumps in incoming observations significantly exceeds the intensity of the change of states of the estimated process. This property makes it possible for the filtering algorithm to process incoming observations using their diffusion approximation. The estimates proposed in this work have the stability property concerning inaccurate knowledge of the distribution of the observed process. To illustrate the robust qualities of the estimates, we present a solution for the applied problem of monitoring the state of an RTP connection based on observations of the packet flow recorded at the receiving node.