This technical note presents necessary and sufficient conditions for 2pth moment stability of several widely used linear stochastic systems. By the matrix derivative operator and vectorial Itô's formula, we first derive two extended systems: one is described by stochastic differential equation (SDE) and the other by ordinary differential equation (ODE). It is shown that the stochastic system is 2pth-moment exponentially stable if and only if the SDE is mean-square exponentially stable or the ODE is exponentially stable. Subsequently, combining the quasi-periodic homogeneous polynomial Lyapunov function methods with the proposed techniques, a series of nonconservative stability criteria are established for linear impulsive, sampled-data, and switched stochastic systems under dwell-time constraints. A numerical example illustrates the proposed theoretical results.