I'm trying to understand each of the above terms, and I'm having a lot of trouble deciphering the difference between them (note, my mathematics training isn't very strong - so please go easy on the jargon / expression with lots of colons and arrows between letters).
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.
Gah! Wikipedia mathematics is brutal...