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I'm trying to understand each of the above terms, and I'm having a lot of trouble deciphering the difference between them.

According to Wikipeda:

  • A Markov chain is a memoryless, random process.

  • A Markov process is a stochastic process, which exhibits the Markov property.

  • The Markov property is the memorylessness of a stochastic property.

  • A stochastic process is a random process, which is a collection of random variables.

  • And finally, random variables are those determined by chance instead of other variables, which seems to mean explicitly that they are memoryless.

Thus, it seems that stochastic process, random process, Markov chain, and Markov process are all the exact same thing... which is a collection of random variables, which are memory-less, which means they exhibit the Markov property.

  • 1
    I had the same problem with the Wikipedia pages on Markov stuff. ARGH.2014-12-11
  • 2
    This is the funniest question I have seen so far in math.exchange!2015-12-15

4 Answers 4