Stochastic Processes I - MIT OpenCourseWare

Lecture 5 : Stochastic Processes I1 Stochastic processA Stochastic process is a collection of random variables indexed by alternate view is that it is a probability distribution over a spaceof paths; this path often describes the evolution of some random value, orsystem, over time. In a deterministic process, there is a fixed trajectory(path) that the process follows, but in a Stochastic process, we do not knowapriori which path we will be given. One should not regard this as havingno information of the path since the information on the path is given bythe probability distribution. For example, if the probability distribution isgiven as one path having probability one, then this is equivalent to having adeterministic process.

Lecture 5 : Stochastic Processes I 1 Stochastic process ... (Stationary) For all h 1 and k 0, the distribution of X k+h X k is the same as the distribution of X h. Proof. The proofs are straightforward and are left as an exercise. Note ... [4]). The lesson to learn is ...

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