Chapter 13
The Strong Markov
Property and Martingale
Problems
Section 13.1 introduces the strong Markov property independence of the past and future conditional on the state at random
(optional) times. It includes an example of a Markov process which
is n
Chapter 15
Convergence of Feller
Processes
This chapter looks at the convergence of sequences of Feller processes to a limiting process.
Section 15.1 lays some ground work concerning weak convergence
of processes with cadlag sample paths.
Section 15.2 sta
Chapter 12
Generators of Markov
Processes
This lecture is concerned with the innitessimal generator of a
Markov process, and the sense in which we are able to write the evolution operators of a homogeneous Markov process as exponentials
of their generator
Chapter 10
Alternative
Characterizations of
Markov Processes
This lecture introduces two ways of characterizing Markov processes other than through their transition probabilities.
Section 10.1 describes discrete-parameter Markov processes as
transformatio
Chapter 4
One-Parameter Processes,
Usually Functions of Time
Section 4.1 denes one-parameter processes, and their variations
(discrete or continuous parameter, one- or two- sided parameter),
including many examples.
Section 4.2 shows how to represent one-
Chapter 5
Stationary One-Parameter
Processes
Section 5.1 describes the three main kinds of stationarity: strong,
weak, and conditional.
Section 5.2 relates stationary processes to the shift operators introduced in the last chapter, and to measure-preservi
Chapter 6
Random Times and Their
Properties
Section 6.1 recalls the denition of a ltration (a growing collection of -elds) and of stopping times (basically, measurable
random times).
Section 6.2 denes various sort of waiting times, including hitting, rst-
Chapter 3
Building Innite Processes
from Regular Conditional
Probability Distributions
Section 3.1 introduces the notion of a probability kernel, which
is a useful way of systematizing and extending the treatment of
conditional probability distributions y