markov process and markov chains

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I have learned that Markov processes are stochastic processes possessing certain mathematical properties (memoryless, etc). My question is, if you say that a process is Markov, is it automatic (as a form of cause and effect) that one can be able to model the process using the Markov Chains? (with the transition probability matrix that has a columns/or rows having a sum of one)?

Your insights would be helpful.