Theorem of Markov

Markov's theorem deals with systems where the future state depends only on the current state, not the sequence of past states. Think of it like a weather model: tomorrow's weather depends only on today's weather, not on the weather days ago. The theorem provides mathematical conditions under which the probabilities of moving from one state to another remain consistent over time. Essentially, it formalizes the behavior of "memoryless" processes, called Markov processes, ensuring their transition probabilities stay constant, which helps in analyzing complex systems like finance, genetics, and queuing networks efficiently.