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In this paper, we study a class of neutral stochastic differential equations (NSDEs) with the cylindrical Brownian motion and Lévy noises in an infinite-dimensional Hilbert space. The existence and uniqueness of the mild solutions to these stochastic differential equations are discussed under assumptions of linear growth on the coefficients. The results of Taniguchi (J. Math. Anal. Appl. 360:245-253, 2009) are generalized and improved as a special case of our theory.

The existence and uniqueness of mild solutions to stochastic differential equations with Lévy noise