  We study the dynamics of classical and quantum systems undergoing a
continuous measurement of position by schematizing the measurement apparatus
with an infinite set of harmonic oscillators at finite temperature linearly
coupled to the measured system. Selective and nonselective measurement
processes are then introduced according to a selection of or an average over
all possible initial configurations of the measurement apparatus. At quantum
level, the selective processes are described by a nonlinear stochastic
Schr\"odinger equation whose solutions evolve into properly defined coherent
states in the case of linear systems. For arbitrary measured systems, classical
behavior is always recovered in the macroscopic limit.
