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Introduction and Preliminaries

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Stochastic Processes

Part of the book series: Mathematics and Its Applications ((MAIA,volume 508))

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Abstract

An outline of the stochastic inference problem, in general terms, is presented in this chapter. This includes the notions of distinctness of hypotheses to be tested as well as the associated parameter estimation from observations. Then, how both these questions can be unified into a broad framework of a decision theory is discussed. These ideas will be elaborated later on and then their application to various classes of stochastic processes will take the center stage.

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References

  1. Fisher, R. A. “On the mathematical foundations of theoretical statistics,” Phil. Trans. Roy. Soc. (London, Ser. A),222 (1921), 309–368.

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  2. On the orthogonality of independent increment processes,“ In Topics in Probability,NYU Courant Inst. (1973), 93–111. Neyman, J., and Pearson, E. S.

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  3. Berger, M. A., and Mizel, V. J. “An extension of the stochastic integral,” Ann. Prob., 10 (1982), 435–450.

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  4. Dvoretzky, A., Kiefer, J., and Wolfowitz, J. “Sequential decision problems for processes with continuous time parameter: problems of estimation,” Ann. Math. Statist. 24 (1953) 403–415.

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© 2000 Springer Science+Business Media Dordrecht

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Rao, M.M. (2000). Introduction and Preliminaries. In: Stochastic Processes. Mathematics and Its Applications, vol 508. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6596-0_1

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  • DOI: https://doi.org/10.1007/978-1-4757-6596-0_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4832-8

  • Online ISBN: 978-1-4757-6596-0

  • eBook Packages: Springer Book Archive

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