Author

J. van Winden

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Preprint Sep 2026

The Schr\"odinger equation with fluctuating nonlinearity in the energy space

We study nonlinear Schr\"odinger equations with nonlinear Stratonovich noise \begin{equation*} \mathrm{d} u\,=\, i\bigl[ \Delta u \,+\, \lambda|u|^{p-1}u\bigr] \, \mathrm{d} t \,+\,i|u|^{(q-1)/2}u\circ \mathrm{d} {W}, \end{equation*} in their energy space $H^1(\mathbb R^d;\mathbb C)$. By combining the stochastic Strich...

Max Sauerbrey, J. van Winden · 0 citations

Preprint Sep 2026

No free lunch for continuity of stochastic convolutions

We construct compact, exponentially stable $C_0$-semigroups $S$ on Hilbert spaces $X$ such that, for every $T>0$, the stochastic convolution $U_g(t)=\int_0^t S(t-s)g(s)\,\mathrm{d}\beta_s $ is unbounded on $[0,T]$ with positive probability for some predictable $g\in L^\infty(\Omega;L^2(0,T;X))$, where $\beta$ is a real...

M. Veraar, J. van Winden · 0 citations