Geometric Moment Contraction for Stochastic Nesterov Acceleration

We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \[ Y_k=Θ_k+β(Θ_k-Θ_{k-1}),\qquad Θ_{k+1}=Y_k-γG(Y_k,X_{k+1}). \] Under mean strong monotonicity and stochastic $L^p$ Lipschitz continuity, an explicit Perron comparison proves synchronous $L^p$ contraction when $βγL_p