# Tagged Questions

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### Transition matrix in left-right hidden semi-Markov model

I'm developing a hidden semi-Markov model left-right . In a left-right model a sequence of $M$ states starts in state $1$ and ends in state $M$, with no repetition of states. Since the model is ...
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### Log-likelihood function

I'm not sure if this could be asked here, or in math overflow... In the following paper Cho, Jin Seo, and Halbert White. "Testing for regime switching." Econometrica 75.6 (2007): 1671-1720. doi: ...
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### Diffusion process. Distribution vs transition probability.

I need confirmation on the following problem: Take a SDE of the form: $$dX_t=a(X_t,t)dt+b(X_t,t)dW_t$$ where all the conditions, such that the solution $X_t$ is defined ...
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### Single evaluation for using exponential sampling until past a point

I am trying to improve an algorithm that looks like the following (and am getting stumped): I am provided with a starting time, rate, and a target time. I then use an exponential distribution to ...
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### How do you explain $f(x_4|x_3)f(x_3|x_2)f(x_2|x_1)f(x_1) = f(x_4,x_3,x_2,x_1)$?

Let $x_1=x(n_1)$, $x_2=x(n_2)$, $x_3=x(n_3)$ and $x_4=x(n_4)$ be random Markov processes $(n_1 < n_2 < n_3 < n_4)$. I don't understand the identity given below on their probability density ...
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### Reversibility of Markov Process and Exponential Distribution of Transition Rates

I am reading the paper Towards Utility-optimal Random Access Without Message Passing by J. Liu, Y. Yi, A. Proutiere, M. Chiang, H. V. Poor. A sentence in Section 3.2 can be paraphrased as follows: ...