this is a mere question of definition, that one surely can figure out by conventional means, but maybe someone can just quickly give me the definition.
What is a memoryless process?
Following the links on memoryless processes on Wikipedia, one arrives at the definition of memorylessness of a random variable. This however is a very different property from the memorylessness of a sequence of random variables, indexed by time. It is often said that Markov processes are memoryless. And vice versa? Do they mean that the Markov property is the memoryless property, i.e.
But then, I also often read in the context of B-processes that they are memoryless. Clearly B-processes are Markov, but with the additional property, that the actual random variables are all independent. So the probability of the present conditioned on any past is just the prob of the present. This would resemble the intuitive meaning for memorylessness the best, but I guess that's not what is meant, right?