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In mathematics, Schilder's theorem is a result in the large deviations theory of stochastic processes. Roughly speaking, Schilder's theorem gives an estimate for the probability that a sample path of Brownian motion will stray far from the mean path. This statement is made precise using rate functions. Schilder's theorem is generalized by the Freidlin–Wentzell theorem for Itō diffusions.
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