A computational tool designed to determine the long-term distribution of a system undergoing Markovian processes. It analyzes a transition matrix, representing probabilities of movement between different states, to identify the stable or equilibrium vector. This vector illustrates the proportion of time the system spends in each state after a prolonged period, assuming the transition probabilities remain constant.
Such a tool is crucial in diverse fields. In finance, it can model market trends. In ecology, it predicts population distributions. In queuing theory, it assesses server utilization. Its origins lie in the development of Markov chain theory, providing a practical application of mathematical models to real-world dynamic systems. The stable vector derived offers insights into system behavior that are not immediately apparent from the transition probabilities alone.
