Toward a theory of nonlinear stochastic systems

The inequalities of Bihari, Langenhop, and Chebyshev are applied to a system of stochastic nonlinear differential equations. As a result, a one-parametric family of determinate estimates from above and below are obtained for the norm of the solution of the system. Each of these estimates is valid with a probability not less than some quantity depending upon the parameter of the family.