STABILITY ANALYSIS OF A STOCHASTIC PORT-HAMILTONIAN CAR-FOLLOWING MODEL

The theorem to prove (Theorem 3.1) states exponential L2-convergence to a Gaussian limit with covariance Σ(∞), uniqueness/ergodicity of the invariant Gaussian law, and an exponential bound for Lipschitz observables; it appears verbatim in the paper, including the setting dR = AR dt + Λ dW, the A = A0 + A1 decomposition, and the spectral bound ā > 0 under γ > 0 and γ/2 + β + Tα > 1/T (see the statement and formulas (25)–(34) and (32)–(33)–(34) in the paper ). The paper proves existence via a time-reversal/start-at-negative-time construction, establishes bounds with an Itô energy inequality, and identifies the invariant Gaussian using characteristic functions and the covariance integral (51)–(53) (and semigroup bounds (41)) . The candidate solution proves the same claims by a standard OU-stationary-covariance construction and synchronous coupling. Aside from minor imprecision about the zero mode (the paper handles it via coordinates so m0 = 0, whereas the candidate briefly declares P = 0, then adds the correct alternative condition on the stable subspace) and a benign notational convention on σ, the arguments agree on all key points and estimates.