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As far as I know, there are three definitions of Markov processes (or of Markov chains). DEFINITION 1 (WEAKER). A process $(X_t)_{t\in[0,\infty)}$ on $(\Omega,\mathcal{F},\mathbb{P})$ with values in ...

Let $X$ be a Markov chain with countable state space $S$ and transition kernel $P$, and let $h \colon S \to [0,1]$ be a sub-harmonic or super-harmonic function. Assume that for all $\varepsilon >0$ ...

This question concerns Feller Markov kernels, similar to Vanessa's question. Terminology By 'Markov kernel' $N:E\to F$, we adopt exactly the same definition as Vanessa, with the exception that $E,F$ ...