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Research Paper#Stochastic Differential Equations, Nonlinear Schrödinger Equation, Mixing Properties🔬 ResearchAnalyzed: Jan 3, 2026 08:53

Polynomial Mixing for Stochastic Schrödinger Equation

Published:Dec 31, 2025 03:42
1 min read
ArXiv

Analysis

This paper investigates the long-time behavior of the stochastic nonlinear Schrödinger equation, a fundamental equation in physics. The key contribution is establishing polynomial convergence rates towards equilibrium under large damping, a significant advancement in understanding the system's mixing properties. This is important because it provides a quantitative understanding of how quickly the system settles into a stable state, which is crucial for simulations and theoretical analysis.
Reference

“Solutions are attracted toward the unique invariant probability measure at polynomial rates of arbitrary order.”

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Research Paper#Financial Mathematics, Portfolio Optimization🔬 ResearchAnalyzed: Jan 3, 2026 15:36

Utility Maximization with Pathwise Constraints in Financial Markets

Published:Dec 30, 2025 17:29
1 min read
ArXiv

Analysis

This paper addresses a practical problem in financial markets: how an agent can maximize utility while adhering to constraints based on pessimistic valuations (model-independent bounds). The use of pathwise constraints and the application of max-plus decomposition are novel approaches. The explicit solutions for complete markets and the Black-Scholes-Merton model provide valuable insights for practical portfolio optimization, especially when dealing with mispriced options.
Reference

“The paper provides an expression of the optimal terminal wealth for complete markets using max-plus decomposition and derives explicit forms for the Black-Scholes-Merton model.”

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