The Global Solutions and Moment Boundedness of Stochastic Multipantograph Equations

Abstract

We consider the existence of global solutions and their moment boundedness for stochastic multipantograph equations. By the idea of Lyapunov function, we impose some polynomial growth conditions on the coefficients of the equation which enables us to study the boundedness more applicably. Methods and techniques developed here have the potential to be applied in other unbounded delay stochastic differential equations.