We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schrödinger equation with nonlinear multiplicative jump noise in the Marcus canonical form. With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to stochastic nonlinear Schrödinger equation in $L^2({\mathbb{R}}^n)$ with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case.

中文翻译：

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由Lévy噪声驱动的随机Strichartz估计和随机非线性Schrödinger方程

我们建立了由跳跃噪声驱动的随机卷积的随机Strichartz估计的新版本，并将其应用于具有Marcus正则形式的非线性乘性跳跃噪声的随机非线性Schrödinger方程。借助确定性Strichartz估计，我们证明了随机非线性Schrödinger方程的整体解的存在性和唯一性。${\mathrm{大号}}^{\mathrm{2个}}（{\mathbb{[R}}^{ñ}）$ 在确定性情况下，在指数的整个亚临界范围内都具有聚焦或散焦非线性。