Understanding Markov Chains and Their Applications

Markov chains predict the future using only the present, completely ignoring the past.

Start by understanding this memoryless property. The probability of moving to the

next state depends solely on where you are now, not how you got there.

First, identify all possible states in your system. Next, determine the transition

probabilities between each state pair. Then, arrange these probabilities into a transition

matrix where rows represent current states and columns show next states. Each row must sum

to one. Multiply your initial state vector by this matrix to predict the next step.

Keep multiplying to see future behavior. Eventually, regular chains reach equilibrium where