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We give necessary and/or sufficient conditions for stochastic stability ofsecond-order linear autonomous systems with parameters, which are perturbed bya random process of the "white noise" type. The Ito's and Stratonovich's formsof stochastic differential equations representing the system with white noiseare considered. The investigation of stochastic stability of the systemsconsidered is based on the construction of special Lyapunov functions in thequadratic forms. The bifurcation value of the white noise intensity at which asystem first becomes unstable is presented in the analytical expression. As anexample a damped harmonic oscillator with randomly perturbed parameters isconsidered.

Stochastic stability criteria for two-dimensional linear autonomous systems perturbed by white noise