Discrete-Time Discrete-Outcome Stochastic Process

A Discrete-Time Discrete-Outcome Stochastic Process is a discrete-time stochastic process that is a discrete-outcome stochastic process.

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• Example(s):
  • a Binomial Process, such as a coin toss sequence.
  • a Roulette Wheel Game.
  • …
• Counter-Example(s):
  • a Continuous-Time Discrete-Event Stochastic Process.
  • a Discrete-Time Continuous-Event Stochastic Process.
  • a Discrete-Time Discrete-Outcome Deterministic Process.
• See: Language Generating System.

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References

2012

• http://en.wikipedia.org/wiki/Stochastic_process#Discrete_time_and_discrete_states
  • QUOTE: If both [math]\displaystyle{ t }[/math] and [math]\displaystyle{ X_t }[/math] belong to [math]\displaystyle{ N }[/math], the set of natural numbers, then we have models which lead to Markov chains. For example:

    (a) If [math]\displaystyle{ X_t }[/math] means the bit (0 or 1) in position [math]\displaystyle{ t }[/math] of a sequence of transmitted bits, then [math]\displaystyle{ X_t }[/math] can be modelled as a Markov chain with 2 states. This leads to the error correcting viterbi algorithm in data transmission.

    (b) If [math]\displaystyle{ X_t }[/math] means the combined genotype of a breeding couple in the [math]\displaystyle{ t }[/math]th generation in a inbreeding model, it can be shown that the proportion of heterozygous individuals in the population approaches zero as [math]\displaystyle{ t }[/math] goes to ∞.

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