Let $(X_{t})_{t \geq 0}$ be a time homogenous Markov process with values in a polish space E and transition kernels $(P_{t})_{t \geq 0}$. Let $B(E,\mathbb{R})$ be the bounded and measureable maps from $E$ to $\mathbb{R.}$ Under which conditions is $(\bar{P}_{t})_{t \geq 0}$ a C0-semigroup where $\bar{P}_{t}:B(E,\mathbb{R}) \rightarrow B(E,\mathbb{R}), \bar{P}_{t}f(x)= \int_{E}f(y)P_{t}(x,dy)$?
2026-03-28 00:36:57.1774658217
When does a Markov process induce a C0-semigroup?
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