# Reflection principle (Wiener process)

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In the theory of probability for stochastic processes, the **reflection principle** for a Wiener process states that if the path of a Wiener process *f*(*t*) reaches a value *f*(*s*) = *a* at time *t* = *s*, then the subsequent path after time *s* has the same distribution as the reflection of the subsequent path about the value *a*.[1] More formally, the reflection principle refers to a lemma concerning the distribution of the supremum of the Wiener process, or Brownian motion. The result relates the distribution of the supremum of Brownian motion up to time *t* to the distribution of the process at time *t*. It is a corollary of the strong Markov property of Brownian motion.