Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
Hu, Y. Z., Wu, F., & Huang, C. M. (2011). General decay pathwise stability of neutral stochastic differential equations with unbounded delay. Acta Mathematica Sinica-English Series, 27(11), 2153 - 2168. https://doi.org/10.1007/s10114-011-9456-5