#### Research Publication Title

Applications of Regular Markov chains

#### Major

Mathematics

#### Faculty Mentor

Dr. Jebessa Mijena

#### Keywords

Markov chain, transition probability, time homogeneity, soccer, weather

#### Abstract

Andrey Markov developed the idea of a Markov chain to model a stochastic process that has the memoryless property, i.e., the probability of each future event depends only on the current event. My research focuses on the applications of a particular type of a Markov chain called a regular Markov chain. Throughout this paper, I will briefly discuss the stochastic process and how a Markov chain could be used in modeling different random processes. In the current paper, Markov chain is used to analyze 21 seasons of the soccer team Real Madrid and all of last year weather in Milledgeville to get future projections of both. In particular, I had to derive a state space for both Real Madrid and the weather of Milledgeville that captured all possible states that they could be in. The state space for Real Madrid is described as a win, draw, or a loss, and for the weather in Milledgeville, the states are sunny, cloudy, or rainy. Finally, I analyzed the transitions between each state to derive a transition probability matrix for both Real Madrid and the weather of Milledgeville and give future projections of Real Madrid and the weather of Milledgeville using the n-step transition probability theorem.

Applications of Regular Markov chains

Andrey Markov developed the idea of a Markov chain to model a stochastic process that has the memoryless property, i.e., the probability of each future event depends only on the current event. My research focuses on the applications of a particular type of a Markov chain called a regular Markov chain. Throughout this paper, I will briefly discuss the stochastic process and how a Markov chain could be used in modeling different random processes. In the current paper, Markov chain is used to analyze 21 seasons of the soccer team Real Madrid and all of last year weather in Milledgeville to get future projections of both. In particular, I had to derive a state space for both Real Madrid and the weather of Milledgeville that captured all possible states that they could be in. The state space for Real Madrid is described as a win, draw, or a loss, and for the weather in Milledgeville, the states are sunny, cloudy, or rainy. Finally, I analyzed the transitions between each state to derive a transition probability matrix for both Real Madrid and the weather of Milledgeville and give future projections of Real Madrid and the weather of Milledgeville using the n-step transition probability theorem.