The authors derive asymptotic behaviors for discrete-time random walks in R^d with polynomial spatio-temporal drifts, finding phase transitions to Gaussian limits in the linear case and three regimes (Gaussian, non-Gaussian SDE stationary, and hypersphere localization) in the nonlinear case under p>
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Limit theorems for random walks with spatio-temporal drift
The authors derive asymptotic behaviors for discrete-time random walks in R^d with polynomial spatio-temporal drifts, finding phase transitions to Gaussian limits in the linear case and three regimes (Gaussian, non-Gaussian SDE stationary, and hypersphere localization) in the nonlinear case under p>