Stochastic processes involve systems that evolve over time (but also more generally in space) according to probabilistic laws. Such systems or models describe the complex phenomena of the real world that have the possibility of being random. These phenomena are more frequent than we can believe. We encounter these phenomena when the quantities we are interested in are not predictable with absolute certainty. However, when such phenomena show a variability of possible outcomes that can be somehow explained or described, then we can introduce a probabilistic model of the phenomenon.
For example, say that we are examining the motion involved in a random walking movement. We study the motion of an object that is constrained to move along a straight line in the two directions allowed. At each movement, it moves randomly to the right or left, each step being...