Markov jump-diffusion models and decision-making-free filtering
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The problem considered is non-linear filtering of Gaussian observations of a Markov jump-diffusion with an embedded Markov chain, that is described by stochastic differential equations driven by Brownian motions and a random Poisson measure. The modelling potential of this class of Markov processes is illustrated by some simple realistic examples.
For the evolution of the conditional expectation of the Markov process decomposed representations are given. They are used as a basis to obtain approximate filtering algorithms that are free of decision making mechanisms. These algorithms are discussed for the examples given.
KeywordsMarkov Chain Markov Process Stochastic Differential Equation Conditional Expectation Embed Markov Chain
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