The paper describes briefly a history of filtering problems of Markov processes and then concentrates on ergodic properties of filtering process. A mistake in a famous Kunita paper on ergodicity of filtering processes is shown. Then the paper reviews various attempts trying to correct this mistake.
Non-markovian queueing systems can be extended to piecewisedeterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.
2018-06-18
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English