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In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by applying J.M.C. Clarks pathwise reformulation technique from the theory of classical nonlinear filtering. The pathwi
We present a closed form solution to the eigenvalue problem of a class of master equations that describe open quantum system with loss and dephasing but without gain. The method relies on the existence of a conserved number of excitation in the Hamil
We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant for the ave
We derive an adiabatic theory for a stochastic differential equation, $ varepsilon, mathrm{d} X(s) = L_1(s) X(s), mathrm{d} s + sqrt{varepsilon} L_2(s) X(s) , mathrm{d} B_s, $ under a condition that instantaneous stationary states of $L_1(s)$ are als
We establish the existence and uniqueness of local strong pathwise solutions to the stochastic Boussinesq equations with partial diffusion term forced by multiplicative noise on the torus in $mathbb{R}^{d},d=2,3$. The solution is strong in both PDE a
The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases ver