  The dynamics of a single microscopic or mesoscopic non quantum system
interacting with a macroscopic environment is generally stochastic. In the same
way, the reduced density operator of a single quantum system interacting with a
macroscopic environment is a priori a stochastic variable, and decoherence
describes only the average dynamics of this variable, not its fluctuations. It
is shown that a general unbiased quantum measurement can be reformulated as a
gambler's ruin problem where the game is a martingale. Born's rule then appears
as a direct consequence of the optional stopping theorem for martingales.
Explicit computations are worked out in detail on a specific simple example.

Quantum Physics