  Quantum systems of interest are typically coupled to several quantum channels
(more generally environments). In this paper, we develop an exact stochastic
Schr\"{o}dinger equation for an open quantum system coupled to a hybrid
environment containing both bosonic and fermionic particles. Such a stochastic
differential equation may be obtained directly from a microscopic model through
employing a classical complex Gaussian noise and a non-commutative fermionic
noise to simulate the hybrid bath. As an immediate application of our developed
stochastic approach, we show that the evolution of the reduced density matrix
can be derived by taking the average over both the bosonic noise and the
fermionic noise. Three specific examples are given in this paper to illustrate
that the hybrid quantum trajectory is fully consistent with the standard
quantum mechanics. Our examples also shed new light on the special features
exhibited by the fermionic bath and bosnoic bath.
