On the stability and boundedness of solutions to certain second order nonlinear stochastic delay differential equations. (English) Zbl 1474.34560
Summary: This paper emphases on stability and boundedness of solutions to certain nonlinear non autonomous second order stochastic delay differential equations. A complete Lyapunov functional is constructed and used to establish conditions, on the nonlinear functions appearing in the equations, to guarantee stability and boundedness of solutions to the second order stochastic delay differential equations considered. The obtained results are new, complement and extend the existing results on second order stochastic delay differential equations in the literature. Finally, examples together with their numerical simulations are given to confirm genuineness and assert the correctness of the obtained results.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65L07 | Numerical investigation of stability of solutions to ordinary differential equations |
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