[TBD]Stochastic process

Introduction

Laymen explanation

Technical explanation

n probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables.

A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set.[4][5] The set used to index the random variables is called the index set.

When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time.[56][57] If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes.

Bernoulli process

One of the simplest stochastic processes is the Bernoulli process,[82] which is a sequence of independent and identically distributed (iid) random variables, where each random variable takes either the value one or zero, say one with probability