The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Levy noise

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 Schrodinger 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 Schrodinger equation in $L^2(R^n)$ with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case. This talk will be based on a joint paper with Wei Liu and Jiahui Zhu.