Skip to main content

Approximation Theoretic Aspects of Probabilistic Representations for Bi-continuous Semigroups

  • Conference paper
  • 1773 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 308))

Abstract

By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-Valued mathematical expectation,the problem of probabilistic approximation for bi-continuous semigroups was studied and the general probabilistic approximation of exponential formulas and the generation theorems were given.

Supported by the fundamental research funds for the central universities (JCB1201B).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kuhnemund: A hille-yosida theorem for bi-continuous semigroups. J. Semigroup Forum 67(2), 205–225 (2003)

    Article  MathSciNet  Google Scholar 

  2. Albanese, A., Mangino, E.: Trotter-Kato theorems for bi-continuous semigroups and applications to Feller semigroups. J. Math. Anal. Appl. 289, 477–492 (2003)

    Article  MathSciNet  Google Scholar 

  3. Khnemund, F., van Neerven, J.: A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions. J. Evol. Equ. 4, 53–73 (2004)

    Article  MathSciNet  Google Scholar 

  4. Jara, P.: Rational approximation schemes for bi-continuous semigroups. Journal of Mathematical Analysis and Applications 344, 956–968 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pfeifer, D.: Approximation-theoretic aspects of probabilistic representations for operator semigroups. Journal of Approximation Theory 43(3), 271–296 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pfeifer, D.: Probabilistic concepts of approximation theory in connection with operation semigroups. J. Approximation Theory and Its Applications 1(4), 93–118 (1985)

    MathSciNet  Google Scholar 

  7. Pfeifer, D., Burter, P.L.: Some general probabilistic estimations for the rate of convergence in operator semigroup representations. Applicable Analysis 23, 111–118 (1985)

    Article  Google Scholar 

  8. Chen, W.-Z.: A representation formula of C infinitesimal generator. Journal of Xiamen University: Nature Science 32(2), 135–140 (1993)

    MATH  Google Scholar 

  9. Chen, W.-Z.: Saturation theorem of probabilistic representation formulas of C-semigroups. Journal of Xiamen University: Nature Science 34(1), 1–6 (1995)

    Google Scholar 

  10. Song, X.-Q., Peng, A.-M.: Probabilistic approximation for C-semigroup and integrated semigroups. Journal of Nanjing University: Mathematical Biquarterly 20(2), 216–225 (2003)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cang, D., Ge, S. (2012). Approximation Theoretic Aspects of Probabilistic Representations for Bi-continuous Semigroups. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34041-3_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34040-6

  • Online ISBN: 978-3-642-34041-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics