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In [[mathematics]] — specifically, in [[stochastic processes|stochastic analysis]] — the '''infinitesimal generator''' of a stochastic process is a [[partial differential operator]] that encodes a great deal of information about the process. The generator is used in evolution equations such as the [[Kolmogorov backward equation]] (which describes the evolution of statistics of the process); its [[Lp space|''L''<sup>2</sup>]] [[Hermitian adjoint]] is used in evolution equations such as the [[Fokker–Planck equation]] (which describes the evolution of the [[probability density function]]s of the process).
{{Citation needed|date=January 2020|reason=There is no citation explaining the general case of an infinitesimal generator}
==Definition==
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