From the 1 of 10 linked papers with an AI index.
10 papers
Infinite-Dimensional Levy Area: Sharp Operator-Ideal Regularity and Anisotropic Ito Geometry
Guangqian Zhao
We prove a sharp universal operator-ideal theorem for infinite-dimensional Lévy area. Every fixed area increment of a continuous locally square-integrable Hilbert-space martingale…
Operational State Selection in Stochastic Analysis: The Least State for a Calibrated Quadratic Ito Program
Guangqian Zhao
We study the least stable state determined by a causal response program and its quantitative calibration. For nondominated families of continuous Hilbert-valued semimartingale laws…
Algebraic Transfer for Operator-Valued Gaussian Chaoses:Oriented Schatten Profiles and Singular Wick Multipliers
Guangqian Zhao
We develop an algebraic transfer calculus for the oriented Schatten profiles of kernels underlying operator-valued Gaussian chaoses. A dimension-free link inequality propagates pro…
Intrinsic Gaussian Tensor Geometry and Random Operator Spectra
Guangqian Zhao
The paper introduces a covariance‑profile technique to build Schatten‑class multiplication operators from Wick powers of Gaussian fields on smooth closed Riemannian manifolds, prov…
A Singular Stochastic Wave--Klein--Gordon System with Rough Gaussian Forcing and Distinct Propagation Speeds
Guangqian Zhao
We construct spatially local paracontrolled solutions on for the stochastic wave--Klein--Gordon system \[ (\partial_t^2-c_{\mathrm{W}}^2Î)u=uv+ξ_{\mathrm{W}},\qqua…
Localized Centered Second-Chaos Operator
Guangqian Zhao
We prove a localized continuous-frequency operator estimate for centered Gaussian chaoses of order two. The result applies to operator-valued centered second chaoses, including Wic…