Skip to main content
SpringerLink
Log in

Dynamical Systems, IID Random Iterations, and Markov Chains

  • Chapter
  • First Online:
Rabi N. Bhattacharya

Part of the book series: Contemporary Mathematicians ((CM))

  • 1021 Accesses

Abstract

The many areas in mathematical statistics, probability theory, statistics processes, and mathematical analysis to which Professor Rabi Bhattacharya has made important and deep contributions include the topics in the title of this paper. In this paper we shall outline some interesting recent results in these topics.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Athreya, K. B. (2004). On Harris irreducibility of iterates of i.i.d. random maps. Tech. Report, Cornell University.

    Google Scholar 

  2. Athreya, K. B. and Dai, J. J. (2000). Random logistic maps - I. J. Th. Prob., 13, 595–608.

    Article  MathSciNet  MATH  Google Scholar 

  3. Athreya, K. B. and Lahiri, S-N. (2006). Measure Theory and Probability Theory. Springer, New York.

    MATH  Google Scholar 

  4. Athreya, K. B. and Ney, P. (1978). A new approach to the limit theory of recurrent Markov chains. TAMS, 245, 493–501.

    Article  MathSciNet  MATH  Google Scholar 

  5. Athreya, K. B. and Roy, V. (2014). Monte Carlo methods for improper target distributions. Electronic Journal of Statistics, 8, 2, 2664–2692.

    Article  MathSciNet  MATH  Google Scholar 

  6. Athreya, K. B., Normand, R., Roy, V. and Wu S-J. (2015). Limit theorems for the estimation of L 1 integrals using Brownian motion. Statistics and Probability Letters, 100, 42–47.

    Article  MathSciNet  MATH  Google Scholar 

  7. Athreya, K. B. and Roy, V. (2015). Estimation of integrals with respect to infinite measures using regenerative sequences. Journal of Applied Probability, 52, to appear.

    Google Scholar 

  8. Athreya, K. B. and Schuh, H.-J. (2003). Random logistic maps - II. The critical case. J. Th. Prob., 16, 4, 813–830.

    Article  MathSciNet  MATH  Google Scholar 

  9. Athreya, K. B. and Stenflo, O. (2003). Perfect sampling for Doeblin chains. Sankhyā A, 65, 4, 763–777.

    MathSciNet  MATH  Google Scholar 

  10. Barnsley, M-F. (1993). Fractals Everywhere, 2nd Edition. Academic Press, New York.

    Google Scholar 

  11. Bhattacharya, R-N. and Rao, B. V. (1993). Random iteration of two quadratic maps. Stochastic Processes, A Festschrift in Honour of G. Kallianpur, 13–22, Springer, New York.

    Google Scholar 

  12. Kifer, Y. (1986). Ergodic Theory of Random Transformations. Birkh’́auser, Boston.

    Google Scholar 

  13. Nummelin, E. (1978). A splitting technique for Harris recurrent Markov chains. Z. W., 43(4), 309–318.

    Article  MathSciNet  MATH  Google Scholar 

  14. Ornstein, D. (1974). Ergodic Theory, Randomness and Dynamical Systems, Yale University Press.

    MATH  Google Scholar 

  15. Wu, W. B. (2001). Iterated random functions, stationarity and central limit theorems. Tech Report, Department of Statistics, University of Chicago.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Iowa State University, Ames, IA, USA

    Krishna B. Athreya

Authors
  1. Krishna B. Athreya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krishna B. Athreya .

Editor information

Editors and Affiliations

  1. Mathematics, The Pennsylvania State University, State College, Pennsylvania, USA

    Manfred Denker

  2. Department of Mathematics, Oregon State University, Corvallis, Oregon, USA

    Edward C. Waymire

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Athreya, K.B. (2016). Dynamical Systems, IID Random Iterations, and Markov Chains. In: Denker, M., Waymire, E. (eds) Rabi N. Bhattacharya. Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-30190-7_8

Download citation

Publish with us

Policies and ethics

Search

Navigation