Dynamic transition probability matrix in markov chains

In summary, a dynamic transition probability matrix is a mathematical tool used in the study of Markov chains to represent the probabilities of transitioning between states in a system that changes over time. It differs from a regular transition probability matrix by taking into account time-dependent changes. Its applications include modeling and analyzing complex systems in various fields, and it is calculated by using transition probabilities at different time points. However, it has limitations such as assuming a Markovian process and requiring a large amount of data.
  • #1
pyrole
3
0
I am intrigued by the idea of changing/dynamic transition probability matrix instead of the assumption of constant transition probability between states.

For eg. Probability of population migrating between 2 states might not remain constant and can be a function of its population or some other factors. Is there a systematic study of this particular category of dynamic or changing transition probabilities in markov processes.
 
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  • #2
You're interested in a topic called "non-homogeneous Markov chains" or "time non-homogeneous Markov chains".

I don't know a good reference that introduces this topic and I don't claim to be able to introduce it myself!
 

What is a dynamic transition probability matrix?

A dynamic transition probability matrix is a mathematical tool used in the study of Markov chains. It represents the probabilities of transitioning from one state to another in a system that changes over time.

How is a dynamic transition probability matrix different from a regular transition probability matrix?

A regular transition probability matrix is static and represents the probabilities of transitioning between states in a system that does not change over time. A dynamic transition probability matrix takes into account the time-dependent changes in the system.

What are the applications of a dynamic transition probability matrix?

A dynamic transition probability matrix is used in various fields, such as engineering, economics, and biology, to model and analyze complex systems that change over time. It is also used in machine learning and data science for predictive modeling.

How is a dynamic transition probability matrix calculated?

A dynamic transition probability matrix is calculated using the transition probabilities between states at different time points. These probabilities are then used to update the matrix, taking into account the changes in the system over time.

What are some limitations of using a dynamic transition probability matrix?

One limitation of a dynamic transition probability matrix is that it assumes a Markovian process, meaning that the transition probabilities only depend on the current state and not on the previous states. It also requires a large amount of data to accurately model complex systems.

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