Skip to main content
Log in

Random difference equations and Renewal theory for products of random matrices

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Bharucha-Reid, A. T., On the theory of random equations.Matscience report 31, Inst. of Math. Sciences, Madras, 1964.

  2. Breiman, L.,Probability. Addison-Wesley Publ. Co., 1968.

  3. Cavalli-Sforza, L. & Feldman, M. W., Models for cultural inheritance, I. Group mean and within group variation.Theor. Population Biol. 4 (1973) plus a sequel, to appear later.

  4. Dunford, N. & Schwartz, J. T.,Linear operators, Vol. I. Interscience Publishers, 1958.

  5. Feller, W.,An introduction to probability theory and its applications, Vol. II,2nd ed. John Wiley & Sons, 1971.

  6. Furstenberg, H. &Kesten, H., Products of random matrices.Ann. Math. Statist. 31 (1960), 457–469.

    MathSciNet  Google Scholar 

  7. Gantmacher, F. R.,The theory of matrices. Chelsea Publ. Co., 1959.

  8. Grenander, U.,Probabilities on algebraic structures, 2nd ed. Almqvist & Wiksell, 1968.

  9. Halmos, P. R.,Lectures on ergodic theory. Chelsea Publ. Co., 1956.

  10. Kaijser, T., Some limit theorems for Markov chains with applications to learning models and products of random matrices. Report Institut Mittag Leffler, 1972.

  11. Kalman, R. E., Control of randomly varying linear dynamical systems.Proc. Symp. Appl. Math. 13 (1962), 287–298, Amer. Math. Soc., 1962.

    MATH  MathSciNet  Google Scholar 

  12. Karlin, S., Positive operators.J. Math. Mech. 8 (1959), 907–937.

    MATH  MathSciNet  Google Scholar 

  13. Kesten, H., Renewal theory for functionals of a Markov chain with general state space. To appear inAnn. Prob.

  14. Kesten, H. &Stigum, B. P., Additional limit theorems for indecomposable multidimensional Galton-Watson processes.Ann. Math. Statist. 37 (1966), 1463–1481.

    MathSciNet  Google Scholar 

  15. Konstantinov, V. M. &Nevelson, M. B., Stability of a linear difference system with random parameters.Mat. Zametki 8 (no. 6) (1970), 753–760; translated inMath. Notes 8 (1970), 895–899.

    MathSciNet  Google Scholar 

  16. Krein, M. G. &Rutman, M. A., Linear operators leaving invariant a cone in Banach space.Uspehi Mat. Nauk 3 (1948), no. 1 (23), 3–95,Amer. Math. Soc. Translations Series 1, Vol. 10, 199–325.

    MathSciNet  Google Scholar 

  17. Meyer, P. A.,Probability and potentials. Blaisdell Publ. Co., 1966.

  18. Parthasarathy, K. R.,Probability measures on metric spaces. Academic Press, 1967.

  19. Paulson, A. S. &Uppuluri, V. R. R., Limit laws of a sequence determined by a random difference equation governing a one-compartment system.Math. Biosci. 13 (1972), 325–333.

    Article  MathSciNet  Google Scholar 

  20. Rosenblatt, M.,Markov processes, Structure and asymptotic behavior. Springer Verlag, 1971.

  21. Rvačeva, E. L., On domains of attraction of multi-dimensional distributions.Lvov. Gos. Univ. Uc. Zap. 29,Ser. Meh. Mat. no. 6 (1954), 5–44;Selected Translations in Math. Statist. and Prob., 2 (1962), 183–205, Amer. Math. Soc.

    Google Scholar 

  22. Solomon, F., Random walks in a random environment. To appear inAnn. Prob.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by the NSF under grant GP 28109 and by a Fellowship from the John Simon Guggenheim Memorial Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kesten, H. Random difference equations and Renewal theory for products of random matrices. Acta Math. 131, 207–248 (1973). https://doi.org/10.1007/BF02392040

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392040

Keywords

Navigation