I Markov Processes: Estimating Transition Probabilities

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Recent discussions focus on estimating transition probabilities for Markov matrices, emphasizing the need for sample data on single-step transitions. Participants highlight the application of Maximum Likelihood Estimation (MLE) for sampling, suggesting the use of sample proportions to determine transition frequencies between states. The calculation involves dividing the number of transitions from state i to j by the total transitions or states for discrete cases, while also considering continuous cases. Additionally, there is interest in mixture models that incorporate Black-Scholes methodologies. The conversation underscores the complexity and various approaches to accurately estimate these probabilities.
WWGD
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Hi,
What are recent results on estimating transition probabilities for Markov matrices. I believe @BvU works in that general area?
 
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Sorry, but: no !
 
WWGD said:
Hi,
What are recent results on estimating transition probabilities for Markov matrices.
Based on what? Do you have sample data of single-step transitions?
 
Are there several options? Im not aware on what area /aspect to sample.I think , yes, iirc, they applied MLE to sample data, but I couldn't come up with the actual statistic .
 
Last edited:
FactChecker said:
Based on what? Do you have sample data of single-step transitions?
Edit: Sample proportions; number of times there has been a transition between states i and j, divided by total number of transitions/states ( for the discrete case)s, or anything else that's available for the continuous case .
 
Last edited:
WWGD said:
Edit: Sample proportions; number of times there has been a transition between states i and j, divided by total number of transitions/states ( for the discrete case)s, or anything else that's available for the continuous case .
I would divide by the number of samples that were in state i before the single step. Also, j=i should be included.
 
Do you know of mixture models that use Black Sholes?
 

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