| Contents |
| Using Lyapunov functions method the sufficient conditions of
stability and asymptotic stability in probability of the integral
manifold of the first order Ito stochastic differential
equations. In this case the random perturbations are assumed from
the class processes with independent increments. The theorems
about stability in probability of the integral manifold of the
first approximation are proved. The problem of stability of
motion's properties given analytically under constantly acting
random perturbations, being small value on the average and damped
perturbations, is solved.
Earlier the stability in probability of the unperturbed motion in
the presence of random perturbations from the class of Wiener
processes (Khas'minskii R.Z., Nevelson M.B., Kushner H.J., Morozan
T., Katz I.J., Krasovskii N.N., Stanzhytskyi A.N.) and also from
the class of processes with independent increments (Gikhman I.I.,
Dorogovtsev A.Y.) were investigated. Also before this the
stability of the integral manifold given analytically of
stochastic differential equations with random perturbations in the
class of Wiener processes (Tleubergenov M.I.) was studied. |
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