Skip to main content
SpringerLink
Log in
Book cover
  • Textbook
  • © 1960

Markov Chains with Stationary Transition Probabilities

Authors:

  1. Kai Lai Chung

    1. Syracuse University, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 104)

Sections

Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
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

Other ways to access

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

Table of contents (37 chapters)

  1. Continuous Parameter

    1. Differentiability

      • Kai Lai Chung
      Pages 130-135

    2. Definitions and measure-theoretic foundations

      • Kai Lai Chung
      Pages 135-143

    3. The sets of constancy

      • Kai Lai Chung
      Pages 143-152

    4. Continuity properties of sample functions

      • Kai Lai Chung
      Pages 152-156

    5. Further specifications of the process

      • Kai Lai Chung
      Pages 156-160

    6. Optional random variable

      • Kai Lai Chung
      Pages 160-168

    7. Strong Markov property

      • Kai Lai Chung
      Pages 168-177

    8. Classification of states

      • Kai Lai Chung
      Pages 177-182

    9. Taboo probability functions

      • Kai Lai Chung
      Pages 182-191

    10. Ratio limit theorems

      • Kai Lai Chung
      Pages 191-196

    11. Discrete approximations

      • Kai Lai Chung
      Pages 196-203

    12. Functionals

      • Kai Lai Chung
      Pages 203-209

    13. Post-exit process

      • Kai Lai Chung
      Pages 209-218

    14. Imbedded renewal process

      • Kai Lai Chung
      Pages 218-224

    15. The two systems of differential equations

      • Kai Lai Chung
      Pages 224-229

    16. The minimal solution

      • Kai Lai Chung
      Pages 229-235

    17. The first infinity

      • Kai Lai Chung
      Pages 235-244

    18. Examples

      • Kai Lai Chung
      Pages 244-261

  2. Back Matter

    Pages 261-278
    PDF
Back to top

About this book

The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an­ swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.
Back to top

Keywords

Back to top

Authors and Affiliations

  • Syracuse University, USA

    Kai Lai Chung

Back to top

Bibliographic Information

Back to top

Publish with us

Policies and ethics

Back to top
Access via your institution

Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
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

Other ways to access

Search

Navigation