By Kardi Teknomo, PhD.

stochastic process

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How do you describe a stochastic process as a simple experiment?

Stochastic process can also be described as a simple experiment (i.e. of tossing a die and coins) with finite number of possible outcomes, which take place in stages (i.e. toss a die first, and if the outcomes are certain numbers such as 4 and 6 then toss the first coin and if the outcome of a coin is head then toss the second coin and if the outcome is a tail, then toss die again and so on). The outcome of one stage depends on the outcome of the previous stages. The probability for each possible outcome at particular stage is known when the outcomes of all previous stages are known. Usually, for Markov Chain, the stages are called time. (Note: if the stages is space, instead of having Markov Chain, we have Markov Random Field) The finite possible outcomes (i.e. head, tail, 1-6 of die) are called states. The variable to locate where we are in the experiment is called random variable.

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Preferable reference for this tutorial is

Teknomo, Kardi. (2017) Stochastic Process Tutorial .