Abstract
This paper considers the generalized Bayesian disorder problem in the discrete time case with two types of the penalty function—the linear and the nonlinear ones. The main results for these cases are given in Theorems 1 and 2, respectively.
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References
Feinberg, E.A., Shiryaev, A.N.: Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings. Stat. Decis. 24, 445–470 (2006)
Pollak, M., Tartakovsky, A.G.: On optimality properties of the Shiryaev-Roberts procedure. Private communication (2008)
Shiryaev, A.N.: On optimal methods in quickest detection problems. Theory Probab. Appl. 8, 22–46 (1963)
Shiryaev, A.N.: Generalized Bayesian nonlinear quickest detection problems: on Markov family of sufficient statistics. In: Mathematical Control Theory and Finance, pp. 377–386. Springer, Berlin (2008)
Shiryaev, A.N.: On stochastic models and optimal methods in the problems of the quickest detection. Teor. Veroyatnost. Primenen. 53, 417–436 (2008). English translation will appear in Theory Probab. Appl.
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Shiryaev, A.N., Zryumov, P.Y. (2009). On the Linear and Nonlinear Generalized Bayesian Disorder Problem (Discrete Time Case). In: Optimality and Risk - Modern Trends in Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02608-9_12
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DOI: https://doi.org/10.1007/978-3-642-02608-9_12
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Print ISBN: 978-3-642-02607-2
Online ISBN: 978-3-642-02608-9
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