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3 questions
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Inhomogeneous Markov chains and the product-integral as a solution to the Kolmogorov forward equation
We have a inhomogeneous continous $K$-State Markov chain $X(t)$ with transition intensity matrix $Q(t)$. Therefore its entries are:
$$q_{ij}(t)= \lim_{\delta \to 0} \frac{1}{\delta} \mathbb{P}(X(t+\...
7
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1
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Does every (generalized?) Markov chain admit transition probabilities?
To pose the question let us start by recalling the following notions:
Transition Probabilities. A transition probability matrix between two measurable spaces $(S,\mathcal{S})$ and $(V,\mathcal{V})$ ...
4
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1
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Practical way to check for geometric convergence
Target distribution is multimodal, 24 dimensions, continuous state space. For MCMC integration (MH sampler) I use a manually tuned proposal distribution.
When I measure the convergence rate ...