Suppose I have a Markov process $X_{t}$ with state space $\Omega$ and generator $L$.
I consider a function $f:\Omega\to\mathbb R$.
Is the couple $(X_t, f(X_t))$ still a Markov process?
If yes, is it possible to construct its generator?
Suppose I have a Markov process $X_{t}$ with state space $\Omega$ and generator $L$.
I consider a function $f:\Omega\to\mathbb R$.
Is the couple $(X_t, f(X_t))$ still a Markov process?
If yes, is it possible to construct its generator?
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