Stochastic Processes pp 106-133 | Cite as

# Markov Transition Functions

## Abstract

Much of the remainder of this book is devoted to Markov processes. A definition of the Markov property was given in Chapter 1, but now we will begin over again in a different spirit. Instead of starting with the general Markov process itself, we will first examine how the transition probability functions of Markov processes can be constructed and studied. While we are doing this in the present chapter and the next one, no probability spaces or random variables will be needed (although the word “probability” will be used informally as a guide to the motivation for the work). Later, in Chapter 8, we will actually construct the processes themselves, and then the connection with the Markov property defined in Chapter 1 will be established.

## Keywords

Markov Chain Markov Process Transition Function Wiener Process Markov Property## Preview

Unable to display preview. Download preview PDF.

## References

- K. L. Chung (1964): “The general theory of Markov Processes according to Doeblin,” Z. Wahrscheinlichkeitstheorie 2, pp. 230–254.CrossRefMATHGoogle Scholar
- A. N. Kolmogorov (1931): „Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung,“. Math. Ann. 104, pp. 415–458.MathSciNetCrossRefMATHGoogle Scholar
- W. Feller (1936): “Zur Theorie der stochastischen Prozesse,” Math. Ann. 113, pp. 113–160.MathSciNetCrossRefGoogle Scholar