Matrix elements stability of quantua stochastic differential equations

The stability of the zero solution of the quantum stochastic differential equation dX(t)=A₁(t)X(t)dB(t)+A₂(t)X(t)dt, in the presence of Fock space white noise B, is defined and studied with the use of the Hudson-Parthasarathy quantum stochastic calculus. An explicit formula is obtained for the solution of the associated initial value problem in the case when A₁, A₂ are compact self-adjoint adapted processes. A variation of parameters formula is obtained in the case of constant A₂.