Solution theory to semilinear stochastic equations of Schr\"odinger type on curved spaces I -- Operators with uniformly bounded coefficients

Alessia Ascanelli; Sandro Coriasco; André Süß

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arXiv · 2207.08428

Solution theory to semilinear stochastic equations of Schr\"odinger type on curved spaces I -- Operators with uniformly bounded coefficients

Alessia Ascanelli·Sandro Coriasco·André Süß

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Abstract

We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy data, and on the spectral measure associated with the noise, such that the Cauchy problem admits a unique function-valued mild solution in the sense of Da Prato and Zabczyc.

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Alessia Ascanelli, Sandro Coriasco, André Süß. 2022-07-18. Solution theory to semilinear stochastic equations of Schr\"odinger type on curved spaces I -- Operators with uniformly bounded coefficients. https://arxiv.org/abs/2207.08428

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