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Stochastische Inversion von Leontief-Matrizen

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Ökonomie und Mathematik
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Zusammenfassung

Einer Leontief-Input-Output-Matrix wird (im Stil der Monte-Carlo-Methode) ein zeitdiskreter Markoff-Prozeß zugeordnet. Mittels dieser Zuordnung wird die Matrixinversion und Lösung der Input-Output-Gleichungen durch gewisse Zufallsvariable auf der Menge der Prozeßtrajekto-rien erwartungstreu geschätzt. Das Verfahren wird exemplarisch anhand von konkretem Datenmaterial vorgeführt.

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Literatur

  1. Berman A, Plemmons RJ (1979) Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York San Francisco London

    Google Scholar 

  2. Bourbaki N (1967) Éléments de mathématique. Théories spectrales. Hermann, Paris

    Google Scholar 

  3. Curtiss JH (1956) A theoretical comparison of the efficiencies of two classical methods and a Monte Carlo method for computing one component of the solution of a set of linear algebraic equations. In: Meyer HA (ed) Symposium on Monte Carlo Methods, pp 191–233, Wiley, New York London

    Google Scholar 

  4. Dorfman R, Samuelson PA, Solow RM (1958) Linear Programming and Economic Analysis. McGraw-Hill, New York Toronto London

    Google Scholar 

  5. Edmundson HP (1953) Monte Carlo matrix inversion and recurrent events. Mathematical Tables and other Aids to Computation 7:18–21

    Article  Google Scholar 

  6. Egle K, Fenyi S (1987) Lösung des DIW Input-Output-Systems durch stochastische Inversion. Discussion Paper. Institut für Wirtschaftstheorie und Operations Research Universität Karlsruhe. In Vorbereitung

    Google Scholar 

  7. Forsythe GE, Leibler RA (1950) Matrix inversion by a Monte Carlo method. Mathematical Tables and other Aids to Computation 4:127–129

    Article  Google Scholar 

  8. Gale D (1960) The Theory of Linear Economic Models. McGraw-Hill, New York Toronto London

    Google Scholar 

  9. Gantmacher FR (1970) Matrizenrechnung. Bd I–II, 3. Auflage. VEB Deutscher Verlag der Wissenschaften, Berlin

    Google Scholar 

  10. Halton JH (1970) A retrospective and prospective survey of the Monte Carlo method. SIAM Review 12:1–63

    Article  Google Scholar 

  11. Hengartner W, Theodorescu R (1978) Einführung in die Monte-Carlo-Methode. Carl Hanser, München Wien

    Google Scholar 

  12. Josifescu M, Tautu P (1973) Stochastic Processes and Applications in Biology and Medicine, vol I, Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  13. Karlin S (1966) A First Course in Stochastic Processes. Academic Press, New York London

    Google Scholar 

  14. Kemeny JG, Snell JL (1965) Finite Markov Chains. Reprint. D Van Nostrand Comp, Princeton, New Jersey

    Google Scholar 

  15. Monte Carlo Method (1951) National Bureau of Standards Applied Mathematics Series (12) Householder AS, Forsythe GE, Germond HH (eds) Washington DC

    Google Scholar 

  16. Nikaido H (1968) Convex Structures and Economic Theory. Academic Press, New York San Francisco London

    Google Scholar 

  17. Rubinstein RY (1981) Simulation and the Monte Carlo Method. Wiley, New York

    Book  Google Scholar 

  18. Wasow WR (1952) A note on the inversion of matrices by random walks. Mathematical Tables and other Aids to Computation 6:78–81

    Article  Google Scholar 

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© 1987 Springer-Verlag Berlin Heidelberg

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Egle, K., Fenyi, S. (1987). Stochastische Inversion von Leontief-Matrizen. In: Opitz, O., Rauhut, B. (eds) Ökonomie und Mathematik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72672-9_19

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  • DOI: https://doi.org/10.1007/978-3-642-72672-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72673-6

  • Online ISBN: 978-3-642-72672-9

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