Stochastic logarithmic Schrodinger equations: energy regularized approach

2021/02/25 by Jianbo Cui, Liying Sun, Cui, Jianbo +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #35Q55 #47J05 #60H15 #81Q05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2102.12607

openalex publication_date 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrödinger (SlogS) equation driven by additive noise or multiplicative noise. The key ingredient lies on the regularized stochastic logarithmic Schrödinger (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of (RSlogS) equations. In addition, temporal Hölder regularity estimates and uniform estimates in energy space \mathbb H¹(\mathcal O) and weighted Sobolev space L²_α(\mathcal O) of the solutions for both SlogS equation and RSlogS equation are also obtained.

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