  We show that quantum probabilities can be derived from statistical mechanics
of classical fields. We consider Brownian motion in the space of fields and
show that such a random field interacting with threshold type detectors
produces clicks at random moments of time. And the corresponding probability
distribution can be approximately described by the formalism of quantum
mechanics. Hence, probabilities in quantum mechanics and classical statistical
mechanics differ not so much as it is typically claimed. The temporal structure
of the "prequantum random field" (which is the $L_2$-valued Wiener process)
plays the crucial role. Moments of detector's clicks are mathematically
described as hitting times which are actively used in classical theory of
stochastic processes. Born's rule appears as an approximate rule. In principle,
the difference between the "precise detection probability rule" derived in this
paper and the conventional Born's rule can be tested experimentally. In our
model the presence of the random gain in detectors playes a crucial role. We
also stress the role of the detection threshold. It is not merely a
technicality, but the fundamental element of the model.
