Nonstationary Stochastic Timing Signatures in the Prompt Gamma-Ray Light Curve of GRB 170817A

Abstract: We investigate time-dependent stochastic structure in the weak prompt gamma-ray emission of GRB 170817A using change-point and deep-kernel Gaussian-process (GP) models. The analysis is based on the 10-300 keV Fermi/GBM light curve with 0.10 s time resolution. Two change-point configurations identify similar covariance transitions at 0.269 and 0.237 s after the gravitational-wave merger, with 10-90% transition widths of 0.441 and 0.393 s, respectively. At the representative gate-defined boundary of t_tr = 0.27 s, all four fixed-split assignments yield positive evidence gains over the full-exposure stationary Matern-3/2 reference. The largest gain is Delta ln Z_split = 5.72 +/- 0.16 for the Matern-3/2 to Matern-3/2 assignment, while the gate-matched damped random walk (DRW) to Matern-3/2 assignment gives Delta ln Z_split = 5.50 +/- 0.16. The fixed-split comparison therefore supports segment-specific covariance evolution without requiring a change of covariance family. The deep-kernel models recover localized time-deformation features peaking at 1.65 and 1.75 s after the merger for DRW and Matern-3/2 base kernels, respectively. Their offsets from the adopted gamma-ray onset at 1.74 s are -0.09 and +0.01 s, both within the 0.10 s sampling resolution. The full-band timing features remain stable when the bin width is changed from 0.10 to 0.12 s, whereas energy subdivision produces larger shifts in gate locations than in warp peaks. Residual diagnostics show that the models reproduce the dominant temporal structure, although localized residual dependence remains. We interpret the gate-defined covariance transition and the localized time-deformation feature as model-dependent phenomenological timing diagnostics. Further simulation calibration and count-level modelling are needed to assess the statistical robustness and physical origin of the recovered nonstationary structure.