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]\displaystyle{ 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):
  • a Continuous-Outcome Stochastic Process.
• See: Discrete State Variable.

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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.

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