Stability and Boundedness of Solutions to a Certain Second-Order Nonautonomous Stochastic Differential Equation | Zendy

A. T. Ademola | Zendy; Sibusiso Moyo | Zendy; B.S. Ogundare | Zendy; M. O. Ogundiran | Zendy; O. A. Adesina | Zendy

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Stability and Boundedness of Solutions to a Certain Second-Order Nonautonomous Stochastic Differential Equation

Author(s) -

A. T. Ademola,

Sibusiso Moyo,

B.S. Ogundare,

M. O. Ogundiran,

O. A. Adesina

Publication year - 2016

Publication title -

international journal of analysis

Language(s) - English

Resource type - Journals

eISSN - 2314-4998

pISSN - 2314-498X

DOI - 10.1155/2016/2012315

Subject(s) - mathematics , lyapunov function , nonlinear system , stability (learning theory) , correctness , order (exchange) , stochastic differential equation , differential equation , stability theory , mathematical analysis , computer science , physics , finance , algorithm , quantum mechanics , machine learning , economics

This paper focuses on stability and boundedness of certain nonlinear nonautonomous second-order stochastic differential equations. Lyapunov’s second method is employed by constructing a suitable complete Lyapunov function and is used to obtain criteria, on the nonlinear functions, that guarantee stability and boundedness of solutions. Our results are new; in fact, according to our observations from the relevant literature, this is the first attempt on stability and boundedness of solutions of second-order nonlinear nonautonomous stochastic differential equations. Finally, examples together with their numerical simulations are given to authenticate and affirm the correctness of the obtained results

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