The infinitesimal generator of a stochastic process is given by $$ Af(x) = \lim_{t \to 0} \frac{\mathbb E_xf(X_t) - f(x)}{t}, $$ I want to find the generator for the sum and difference of independent Markov processes, $X_t \pm Y_t$. I remember reading somewhere that the sum of the generators is the generator of the sum but can't seem to prove it. Is that correct? Can anyone please provide some reference for this?
2026-03-31 17:58:48.1774979928
Generator of sum of independent Markov processes
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