Abstract
Let x t be a temporally homogenous Markov process with state space S, called a system process in this paper. Suppose that we want to observe the sample path x t , but what we can observe is a stochastic process Y t of the form
where h is a continous function on S and N t is a standard Brownian motion independent of x s . The filtering of the system based on the observation data Y t is defined by a conditional distribution
where A is a Borel subset of S and
Keywords
- Markov Process
- Invariant Measure
- Stochastic Differential Equation
- Nonnegative Solution
- Standard Brownian Motion
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References
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© 1991 Springer Science+Business Media New York
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Kunita, H. (1991). Ergodic Properties of Nonlinear Filtering Processes. In: Alexander, K.S., Watkins, J.C. (eds) Spatial Stochastic Processes. Progress in Probability, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0451-0_11
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DOI: https://doi.org/10.1007/978-1-4612-0451-0_11
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