I'm learning stochastic process in college. How to understand Markov property?I'm curious about what is the power and validity of Markov property ?
A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state, not on the sequence of events that preceded it.
The question is big and perhaps vague. To be specific and clear, I'd like to illustrate some aspects of the question.
- Why we need such property? Why is it essential and ubiquitous? What is the "philosophy" of such property?
- Is this property an assumption when modelling? If it is, does it hold necessarily? If it does not hold, what's the influence?