Abstract
A martingale is a stochastic process that encodes a kind of fairness or unbiasedness, which is associated with a reference process. Here we show that, if the reference process x_{t} evolves according to the Langevin equationwith drift a(x) and if a(x_{t}) is a martingale, then its amplitude is the Langevin function, which originally described the canonical response of a single classical Heisenberg spin under static field. Furthermore, the asymptotic limit of x_{t}/t obeys the ensemble statistics of such a Heisenberg spin.
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