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Preprint Sep 2026

Polynomial mixing for the weakly damped stochastic nonlinear Schr\"odinger equation on the whole space

We consider the weakly damped stochastic nonlinear Schr\"odinger (NLS) equation on the real line, driven by a noise that is white in time and smooth in space. Assuming that the noise is sufficiently non-degenerate, we prove that the equation has a unique stationary measure in the class of probability measures concentra...

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Preprint Aug 2026

Logarithmic derivatives of variational and singular stochastic partial differential equations

For a stochastic partial differential equation posed on a Gelfand triple and satisfying the fully local monotone conditions of R\"ockner, Shang and Zhang, we compute the logarithmic derivative of the law of the solution at a fixed time along a prescribed direction of the state space. The formula is intrinsic, being exp...

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Preprint Oct 2026

Large Deviations of Invariant Measures of Fractional Reaction-Diffusion Equations Driven by Multiplicative Noise on R^n

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Open access Aug 2026

Variation of Constants for Riemann--Liouville Fractional Stochastic Differential Equations with Sharp $L^2$-Threshold and Optimal Regularity

We develop a rigorous analytical framework for Riemann-Liouville fractional  stochastic differential equations (RL-FSDEs), addressing a gap in the literature where existing treatments either focus on Caputo formulations or  provide incomplete existence arguments. Our approach combines Laplace transform operational calc...

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Preprint Oct 2026

Fundamental solution expansions in stochastic homogenization of parabolic systems with time-dependent coefficients

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Preprint Oct 2026

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For weak solutions to quasilinear degenerate parabolic equations of $p$-Laplace type, a central obstacle in applying the method of intrinsic scaling to prove their H\"{o}lder regularity is the derivation of forward-in-time propagation estimate for the spatial measure of level sets. In this paper, we revisit and overcom...

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