Infinitesimal generator (stochastic processes) (source code)

= Infinitesimal generator
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{wiki}

For a Markov process with transition semigroup $(P_t)$, its infinitesimal generator is the operator
$$
Lf=\lim_{t\downarrow0}\frac{P_tf-f}{t}
$$
on the functions for which this limit exists.

= Infinitesimal generator
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