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The Wiener-Hopf Technique in Applied Probability

Published online by Cambridge University Press:  05 September 2017

Abstract

In this study some of the basic ideas needed for the application of the Wiener-Hopf Technique in solving problems occurring in applied probability theory are discussed; the paper aims to give a short introduction. The method is illustrated by applying it to two problems; one, although basic in probability theory, is rather simple to handle by this method. The second is much more intricate, but shows clearly the power of the method.

Type
Part IV — Mathematical Methods in Probability and Statistics
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Noble, B. (1958) The Wiener-Hopf Technique. Pergamon Press, London.Google Scholar
[2] Kemperman, J. H. B. (1961) The Passage Problem for a Stationary Markov Chain. The University of Chicago Press, Chicago.CrossRefGoogle Scholar
[3] Arrow, K. J., Karlin, S. and Scarf, H. (1958) Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford.Google Scholar
[4] Arrow, K. J., Karlin, S. and Scarf, H. (1962) Studies in Applied Probability and Management Science. Stanford University Press, Stanford.Google Scholar
[5] Cohen, J. W. (1969) The Single Server Queue. North-Holland Publ. Co., Amsterdam.Google Scholar
[6] Cohen, J. W. (1969) Single server queues with restricted accessibility. J. Engin. Math. 3, 265284.CrossRefGoogle Scholar
[7] Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
[8] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.Google Scholar
[9] Titchmarsh, E. C. (1952) Theory of Functions. Oxford University Press, London.Google Scholar
[10] Whittaker, E. T. and Watson, G. N. (1946) A Course of Modern Analysis. Cambridge University Press, London.Google Scholar
[11] Keilson, J. (1965) Green's Function Method in Probability Theory. Griffin, London.Google Scholar