Stochastic logarithmic Schr\"odinger equations driven by L\'evy noise
Jiahui Zhu, Jianliang Zhai
TL;DR
This paper investigates the stochastic logarithmic Schr"odinger equation influenced by Le9vy noise, establishing global well-posedness in an Orlicz space through regularization and convergence analysis.
Contribution
It introduces a novel approach to prove well-posedness of the stochastic logarithmic Schrf6dinger equation with Le9vy noise in an Orlicz space, using regularization techniques.
Findings
Proved global existence and uniqueness of solutions.
Established convergence of regularized solutions.
Extended analysis to equations with saturated nonlinear multiplicative Le9vy noise.
Abstract
In this paper, we study the stochastic logrithmic Schr\"odinger equation with saturated nonlinear multiplicative L\'evy noise. The global well-posedness is established for the stochastic logrithmic Schr\"odinger equation in an appropriate Orlicz space by construct solutions of a regularized equation converging strongly to a solution to the original equation.
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Taxonomy
TopicsStochastic processes and financial applications · Numerical methods in inverse problems · Spectral Theory in Mathematical Physics