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Idempotent splitting for Markov kernels

I do not know if the result is new or not. But I believe the problem is easy if you think in terms of the Eilenberg-Moore category of the Giry monad. Since that category is isomorphic to a certain ...
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Connection between invariant measure and positive recurrence for continuum state space markov chain

Yes, let's assume that sup (which I think should be in the denominator in the last expression) is finite, as otherwise it is always true. Suppose it is bounded by A, the each return time is also ...
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Average and max. hitting time to a specific vertex

Notation: Let $G=(V,E)$ be an undirected simple graph of $n$ nodes. If $\tau_x$ is the (random) time it takes the walk to reach the node $x$, then write $H(v,x)=E_v(\tau_x)$. Denote $H_{\max}(x):=\...
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What is the significance of Blumenthal and Getoor's result on the boundedness of paths of a standard Markov process?

It's a simple fact, but not quite as simple as you claim. For example, the function $$ x: [a,b] \to \mathbb R\cup\{\pm\infty\} : t\mapsto \frac 1 {b-t} $$ is càdlàg but not bounded. The rough ...
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