  We consider an equation of the geodesic deviation appearing in the problem of
gravitational wave detection in an environment of gravitons. We investigate a
state-dependent graviton noise (as discussed in a recent paper of
Parikh,Wilczek and Zahariade) from the point of view of the Feynman integral
and stochastic differential equations. The evolution of the density matrix and
the transition probability in an environment of gravitons is obtained. We
express the time evolution by a solution of a stochastic geodesic deviation
equation with a noise dependent on the quantum state of the gravitational
field.
