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 be a probability space and (An) a sequence of events in .
– The set of ω ∈ Ω belonging to an infinity of An, that is,
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,
is called the lower limit of the sequence (An).
THEOREM 1.1.– (Borel-Cantelli lemma) Let (An) be a sequence of events in .
1. , them
2. and (An) is a sequence of independent events, then
Let (Xn) be a ...