We study the theoretical guarantees of system identification methods for a class of unknown nonlinear systems in stochastic settings, incorporating analytic functions in the presence of disturbances. Within this framework, we explore two primary system identification methods: least-squares estimator (LSE), classified as point estimators, aimed at estimating a specific point within a parameter space, and set-membership estimator (SME) , classified as set estimators, which estimate a set to ensure inclusion of the true parameters. Both approaches rely on sample data generated by the system. Despite the widespread application of such estimators, their non-asymptotic guarantees within a nonlinear framework in stochastic settings remain limited. Specifically, we provide probabilistic guarantees for error bounds of LSE and for the diameters of sets estimated by SME. Our analysis is grounded in probabilistic persistent excitation within these nonlinear systems with i.i.d. noises. We demonstrate numerical experiments showcasing the system identification of systems such as pendulum and quadrotor.