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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0004-0002

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

Derivatives of Markov kernels and their Jordan decomposition

Autorzy Heidergott, B.  Hordijk, A.  Weisshaupt, H. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed.
Słowa kluczowe
PL rozkład Jordana  
EN Markov kernels   weak differentiation   Jordan decomposition  
Wydawca Walter de Gruyter GmbH & Co. KG
Czasopismo Journal of Applied Analysis
Rocznik 2008
Tom Vol. 14, nr 1
Strony 13--26
Opis fizyczny Bibliogr. 14 poz.
Twórcy
autor Heidergott, B.
autor Hordijk, A.
autor Weisshaupt, H.
  • Vrije Universiteit Amsterdam. Department of Econometrics, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands, bheidergott@feweb.vu.nl
Bibliografia
[1] Dieudonne, J., Grundzuege der modernen Analysis. Band 2 (German), 2nd ed., translated from the third French edition by L. Boli and H. Aritelmann, ("Foundamentals of modern analysis. Vol. 2"), VEB Deutscher Verlag der Wissenschaften, Berlin, 1987.
[2] Dudley, R. M., Real Analysis and Probability, Revised reprint of the 1989 original, Cambridge Stud. Adv. Math. 74, Cambridge Univ. Press, Cambridge, 2002.
[3] Heidergott, B., A weak derivative approach to optimization of threshold parameters in a multi-component maintenance system, J. Appl. Probab. 38 (2001), 386-406.
[4] Heidergott, B., Option pricing via Monte Carlo simulation: A weak derivative approach, Probab. Engrg. Inform. Sci. 15 (2001), 335-349.
[5] Heidergott, B., Hordijk, A., Weisshaupt, H., Measure-valued differentiation for stationary Markov chains, Math. Oper. Res. 31 (2006), 154-172.
[6] Karatzas, L, Shreve, S. E., Brownian Motion and Stochastic Calculus, 2nd ed., Grad. Texts in Math. 113, Springer-Verlag, New York, 1991
[7] Pflug, G., Optimisation of Stochastic Models, Kluwer Academic Publishers, Boston, 1996.
[8] Pflug, G., Weisshaupt, H., Probability gradient estimation by set-valued calculus and aplications in network design, SIAM J. Optim. 15 (2005), 898-914.
[9] Segal, I., Kunze, R., Integrals and Operators (second revised and enlarged edition), Springer, Berlin, 1978.
[10] Schervish, M., Theory of Statistics. Springer, New York, 1995.
[11] Weisshaupt, H., A measure-valued approach to convex set-valued dynamics, Set-Valued Anal. 9 (2001), 337-373.
[12] Weisshaupt, H., A characterization of parallelepipeds related to weak derivatives, Acta Math. Hungar. 107 (2005), 319-328.
[13] Weisshaupt, H., A generalization of Lehmann's theorem on the comparison of uniform location experiments, Acta Math. Hungar. 107 (2005), 329-336.
[14] Willard, S., General Topology, Addison-Wesley Publishing, Co, Reading, MA, 1970.
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