  A *-algebraic indefinite structure of quantum stochastic (QS) calculus is
introduced and a continuity property of generalized nonadapted QS integrals is
proved under the natural integrability conditions in an infinitely dimensional
nuclear space. The class of nondemolition output QS processes in quantum open
systems is characterized in terms of the QS calculus, and the problem of QS
nonlinear filtering with respect to nondemolition continuous measurments is
investigated. The stochastic calculus of a posteriori conditional expectations
in quantum observed systems is developed and a general quantum filtering
stochastic equation for a QS process is derived. An application to the
description of the spontaneous collapse of the quantum spin under continuous
observation is given.
