Stochastically bounded solutions of a nonlinear stochastic differential equations

Sufficient and necessary conditions for the existence of a stochastically bounded solution of a nonlinear nonhomogeneous stochastic differential equation are found. The stationary and periodic cases are also considered. The results in [O.V. Il’chenko, Stochastically bounded solutions of a linear homogeneous stochastic differential equation, Theor. Probab. Math. Statist. 68 (2004) 41–48] are generalized.