Chapter 1

Introduction to Stochastic Processes

In this introductory chapter we present some notions regarding sequences of random variables (r.v.) and the most important classes of random processes.

1.1. Sequences of random variables

Let image be a probability space and (An) a sequence of events in image.

– The set of ω ∈ Ω belonging to an infinity of An, that is,

image

is called the upper limit of the sequence (An).

– The set of ω ∈ Ω belonging to all An except possibly to a finite number of them, that is,

image

is called the lower limit of the sequence (An).

THEOREM 1.1.– (Borel-Cantelli lemma) Let (An) be a sequence of events in image.

1. image, them image

2. image and (An) is a sequence of independent events, then

Let (Xn) be a ...

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