10 papers
Infinite-Dimensional Levy Area and Spectral Ancestry
Guangqian Zhao
We relate primitive ancestry in free-Lie expansions of infinite-dimensional Lévy area to critical weak-Schatten spectra. For , , and $J=\ker(T(V)\to S(V)…
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…
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}}^2Δ)u=uv+ξ_{\mathrm{W}},\qquad…
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…
Gaussian Operator Algebras: Observability, Reconstruction, and Microscopic Limits
Guangqian Zhao
We reconstruct Gaussian operator algebras from finite source-labelled observations, recovering coefficients, ordinary multiplication, and completion in independently specified Scha…