  In this article, we derive the stochastic master equations corresponding to
the statistical model of a heat bath. These stochastic differential equations
are obtained as continuous time limits of discrete models of quantum repeated
measurements. Physically, they describe the evolution of a small system in
contact with a heat bath undergoing continuous measurement. The equations
obtained in the present work are qualitatively different from the ones derived
in \cite{A1P1}, where the Gibbs model of heat bath has been studied. It is
shown that the statistical model of a heat bath provides clear physical
interpretation in terms of emissions and absorptions of photons. Our approach
yields models of random environment and unravelings of stochastic master
equations. The equations are rigorously obtained as solutions of martingale
problems using the convergence of Markov generators.
