Derivatives of Markov kernels and their Jordan decomposition

• Autorzy: Heidergott B. , Hordijk A. , Weisshaupt H.
• 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

EN

Markov kernels; weak differentiation; Jordan decomposition

PL

rozkład Jordana

• Wydawca: De Gruyter
• 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,

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.