Abstract
In the paper we define the Dawson-Watanabe type superprocesses in random environment as solutions to the related martingale problems. An environment is modelled by a finite state time homogeneous Markov process with the given transition probability intensity matrix. A system of nonlinear stochastic equations is derived for a posteriori probabilities. Reduced system of linear equations is also obtained.
Mathematics Subject Classification (2010): 60J70, 60K37
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Grigelionis, B. (2013). On the Nonlinear Filtering Equations for Superprocesses in Random Environment. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_16
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DOI: https://doi.org/10.1007/978-3-642-33549-5_16
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