Some Basic Tools

This chapter has two objectives. The first is to introduce some tools which will be used frequently in succeeding chapters. These tools will be illustrated here with applications to countable state Markov chains. The hope is that after seeing how they are applied in this familiar setting, the reader will be better prepared to appreciate their usefulness in the context of particle systems. The second objective of this chapter is to prove some nonstandard results about Markov chains which we will need in later chapters. The material in the first five sections relates primarily to the first objective, while the latter sections relate to the second objective.