Markov Chain Simulation Program with MATLAB Implementation

To execute the original Markov chain simulation program within the MATLAB environment, follow these technical steps. First, verify that you have MATLAB R2020b or later installed with Statistics and Machine Learning Toolbox. Download the simulation package containing main.m, transitionMatrix.m, and simulateChain.m functions from the repository. In MATLAB, navigate to the project directory and initialize the simulation by calling main() function which handles parameter configuration and visualization setup. The core algorithm utilizes state transition matrices to model probabilistic system behavior through iterative matrix multiplication. Key functions include: - transitionMatrix.m: Defines state transition probabilities using stochastic matrix normalization - simulateChain.m: Implements Markov process iteration with Monte Carlo methods - plotResults.m: Generates visualizations of state evolution and stationary distributions After running the program, observe real-time animation of state transitions and analyze convergence properties. The simulation outputs include transition graphs, steady-state probability calculations, and statistical metrics for stochastic system analysis. These results enable quantitative assessment of system dynamics through eigenvalue decomposition of transition matrices and hitting time computations, supporting data-driven decisions in stochastic modeling applications.