Markov Chain Model Calculator
Easily calculate state probabilities over time with our Markov Chain Model Calculator. Enter your transition matrix, initial state, and steps to visualize the probability distribution.
Input Parameters
Enter a square matrix as a JSON array of arrays.
Enter the initial state as a JSON array (vector).
Number of time steps to simulate.
State Probabilities Over Time
Probability Visualization
Understanding Markov Chains
A Markov Chain is a mathematical system that transitions from one state to another. It's a 'memoryless' process, meaning the next state depends only on the current state, not on the sequence of events that preceded it. They are used to model the probability of events where future states depend only on the present state. For example, predicting weather, stock prices, or customer behavior. The transition matrix defines the probabilities of moving between states, and by applying it iteratively to an initial state, we can see how probabilities evolve over time. This tool helps visualize this evolution.
- Transition Matrix: Probabilities of moving from one state to another.
- Initial State: Starting probabilities across all states.
- Steps: Number of time periods to project probabilities forward.