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October 20, 2025Open Access

An inductive approach to stochastic estimates for the φ^4₂-equation with correlated coefficient field

Puntos clave

Our method enhances stochastic estimates for the φ^{4}_2-equation, revealing new pathways for analysis.
The stochastic estimates leverage Gaussian integration and Wick products for accurate results.
Mollifications of space-time white noise play a crucial role in the approach's effectiveness.
Correlated coefficient fields introduce complexity but enable deeper insights into stochastic behavior.

Resumen

We develop an inductive approach to obtaining stochastic estimates for the φ^4₂-equation when the coefficient field is correlated with the driving noise. Our method is based on (infinite-dimensional) Gaussian integration by parts with respect to Wick products of Gaussian random variables (more precisely, mollifications of space-time white noise)

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Cite This Study

Nicolas Clozeau (Sun,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac362ac https://doi.org/https://doi.org/10.48550/arxiv.2509.11309

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