FAQ About Stats related questions

A Markov chain is a stochastic process that satisfies the Markov property. This property states that the probability of a future state depends only on the current state, and not on the past states.

Markov chains are used in a variety of applications, including:

• Finance: Markov chains can be used to model the price of stocks and other financial assets., Car insurance etc
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A Markov chain is a discrete-time stochastic process. This means that the states of the process are discrete, and the time between transitions is discrete.

The states of a Markov chain can be anything, but they are often numbers. For example, the states of a Markov chain that models the price of a stock could be the stock's price at the end of each day.

The transition probabilities of a Markov chain are the probabilities of transitioning from one state to another. For example, the transition probabilities of a Markov chain that models the price of a stock could be the probabilities of the stock's price increasing, decreasing, or staying the same.

The Markov property states that the probability of a future state depends only on the current state, and not on the past states. This means that the past states are irrelevant to the future states, given the current state.

The Markov property is a powerful tool that can be used to simplify the analysis of Markov chains. It allows us to ignore the past states and focus on the current state.

There are two types of Markov chains:

• Discrete-time Markov chains: These chains have a discrete number of states and a discrete time step.
• Continuous-time Markov chains: These chains have a continuous number of states and a continuous time step.

Discrete-time Markov chains are more common than continuous-time Markov chains. They are easier to analyze and simulate.

Markov chains are a powerful tool that can be used to model a variety of phenomena. They are used in a variety of applications, including finance, engineering, medicine, and computer science.