On a type of stochastic differential equations driven by countably many Brownian motions

Consider the one-dimensional SDE Xt=x+∑i=1∞∫0tσi(Xs) dWsi+∫0tb(Xs) ds, where Wi is an infinite sequence of independent standard Brownian motions, i=1,2,3,… . We prove two theorems on the existence and uniqueness of solutions with non-Lipschitz coefficients, and give a non-contact property and a strong comparison theorem for solutions.