Abstract
The main subject of this chapter is a class of random sequences that are defined in terms of random walks T = (T m : m = 0, 1, 2,...) in ℤ̄+ satisfying Tm+1 (ω) ≥ 1 + T m(ω) (with the understanding that ∞ ≥ 1 + ∞).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Athreya, K. B. and Ney, P. E., Branching Processes, Springer-Verlag, New York, 1972.
Blumenthal, R. M. and Getoor, R. K., Markov Processes and Potential Theory, Academic Press, New York, 1968.
Chen, Mu Fa, From Markov Chains to Non-Equilibrium Particle Systems, World Scientific, Singapore, 1992.
Chow, Y. S. and Robbins, Herbert and Siegmund, David, Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston, 1971.
Chung, Kai Lai, Markov Chains with Stationary Transition Probabilities, Second Edition, Springer-Verlag, New York, 1967.
Chung, Kai Lai, Lectures on Boundary Theory for Markov Chains, Princeton University Press, Princeton, New Jersey, 1970.
Dellacherie, Claude and Meyer, Paul-André, Probabilities and Potential C (translated from French), Elsevier Science Publishers B. V., Amsterdam, 1988.
Dellacherie, Claude and Meyer, Paul-André, Probabilités et Potential (Théorie du potentiel associée à une résolvante, Théorie des processus de Markov), Hermann, Paris, 1987.
Doob, J. L., Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, New York, 1984.
Doyle, Peter G. and Snell, J. Laurie, Random Walks and Electric Networks, Mathematical Association of America, 1984.
Dynkin, E. B., Markov Processes, Vol. I, Academic Press, New York, 1965.
Dynkin, E. B., Markov Processes, Vol. II, Academic Press, New York, 1965.
Dynkin, Evgenii B. and Yushkevich, Alexsandr A., Markov Processes: Theorems and Problems, Plenum Press, New York, 1969.
Edgar, G. A. and Sucheston, Louis, Stopping Times and Directed Processes (Encyclopedia of Mathematics and Its Applications, Vol. 47), Cambridge University Press, Cambridge, 1992.
Ethier, Stewart N. and Kurtz, Thomas G., Markov Processes: Characterization and Convergence, John Wiley & Sons, New York, 1986.
Preedman, David, Approximating Countable Markov Chains, Holden-Day, San Francisco, 1971.
Preedman, David, Markov Chains, Holden-Day, San Francisco, 1971.
Harris, Theodore E., The Theory of Branching Processes, Dover, New York, 1989.
Hughes, Barry D., Random Walks and Random Environments, Vol. 1: Random Walks, Clarendon Press, Oxford, 1995.
Hughes, Barry D., Random Walks and Random Environments, Vol. 2: Random Environments, Clarendon Press, Oxford, 1996.
Iosifescu, Marius, Finite Markov Processes and Their Applications, John Wiley & Sons, Chichester, 1980.
Kalashnikov, Vladimir V., Topics on Regenerative Processes, CRC Press, Boca Raton, Florida, 1994.
Kemeny, John G. and Snell, J. Laurie and Knapp, Anthony W., Denumerable Markov Chains, D. van Nostrand, Princeton, New Jersey, 1966.
Kingman, J. F. C., Regenerative Phenomena, John Wiley & Sons, London, 1972.
Lawler, Gregory F., Intersections of Random Walks, Birkhäuser, Boston, 1991.
Maisonneuve, Bernard, Systèmes Régénératifs (Astérique, Vol. 15), Société Mathématique de France, Paris, 1974.
Révész, Pál, Random Walk in Random and Non-Random Environments, World Scientific, Singapore, 1990.
Sharpe, Michael, General Theory of Markov Processes, Academic Press, Boston, 1988.
Spitzer, Frank, Principles of Random Walk, Second Edition, Springer-Verlag, New York, 1976.
Tackás, Lajos, Combinatorial Methods in the Theory of Stochastic Processes, John Wiley & Sons, New York, 1967.
Yang, Xiang-qun, The Construction Theory of Denumerable Markov Processes, John Wiley & Sons, Chichester, 1990.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fristedt, B., Gray, L. (1997). Renewal Sequences. In: A Modern Approach to Probability Theory. Probability and its Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2837-5_25
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2837-5_25
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-2839-9
Online ISBN: 978-1-4899-2837-5
eBook Packages: Springer Book Archive