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Tytuł artykułu

Derivatives of Markov kernels and their Jordan decomposition

Identyfikatory
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.
Wydawca
Rocznik
Strony
13--26
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0004-0002
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