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Let $(B_t)_{t\geq0}$ be a one-dimensional, standard Brownian motion and let $(l(0,t))_{t\geq0}$ be its local time at the origin. The process $((B_t,l(0,t)))_{t\geq0}$ is a markov process on $\mathbb{R}\times\mathbb{R}_+$. Which is its infinitesimal generator?

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    Not every Markov process has an infinitesimal generator, only (Itô) diffusions have. What makes you think (B,L) is a diffusion?2011-07-30

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