# Discrete-Outcome Stochastic Process

A Discrete-Outcome Stochastic Process is a stochastic process that is a discrete-outcome process (such as from a discrete random variable).

**Context:**- It can range from being a Discrete-Outcome Discrete-Time Stochastic Process to being a Discrete-Outcome Continuous-Time Stochastic Process.
- It can (typically) be represented partly by a Discrete Probability Function.

**Example(s):**- a Binomial Process, [math]B(n,p)[/math].
- a Markov Process, that can be modeled by a Markov chain.
- a Random Walk/Random Walker.
- a Chinese Restaurant Process.

**Counter-Example(s):****See:**Discrete State Variable.

## Referemces

### 2007

- Joseph C. Watkins. (2007). “Discrete Time Stochastic Processes."
- QUOTE: A stochastic process X (or a random process, or simply a process) with index set � and a measurable state space (S, B) defined on a probability space (,F, P) is a function X : � × ! S such that for each � 2 �, X(�, ·) : ! S is an S-valued random variable. Note that � is not given the structure of a measure space. In particular, it is not necessarily the case that X is measurable. However, if � is countable and has the power set as its �-algebra, then X is automatically measurable.