Author

O. J. Assaad

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Preprint Aug 2026

Weak limits of multiple Wiener integrals: representation, extraction, and realization

We study weak limits of multiple Wiener integrals together with the limits of their kernel contractions. After passage to a subsequence, bounded kernel sequences admit a Gaussian Hermite representation whose coordinates carry weights determined by the original chaos orders. In the limits of kernel contractions, only pa...

O. J. Assaad · 0 citations

Preprint Aug 2026

Finite Gaussian Reconstruction of Polynomial Orbits: From Correlated Moments to Oscillatory Periods

Let $P$ be a real polynomial of degree at most $m$ on $\mathbb{R}^d$, and let $X$ be standard Gaussian. Because Gaussian observations are invariant under $O(d)$, the natural inverse problem is to recover the orthogonal orbit of $P$; the law of $P(X)$ alone is generally insufficient. We prove that a prescribed finite fa...

O. J. Assaad · 0 citations

Preprint Aug 2026

Weak Limits of Wiener Chaos: Primitive-Fock Classification and Hilbert-Stein Extraction

We characterize the weak closure of uniformly $L^2$-bounded vectors in a fixed Wiener chaos when the underlying Gaussian Hilbert spaces may vary. On a represented subsequence, each physical-weight tensor space splits into a decomposable closed span and its primitive orthogonal complement. Primitive-block evaluation ext...

O. J. Assaad · 0 citations