Work

Geometry property of stochastic parabolic equations and Prékopa-Leindler inequality on bounded domains

Year: 2026

Type: preprint

Abstract: We study the preservation of spatial concavity and log-concavity for stochastic parabolic equations posed on bounded convex domains. For the linear noise, by using Minkowski convolutions, we establish the convexity preservation of solution almost surely. For the nonlinear noise, by using Itô formula, the impact of noise is given. Moreover, we establish the relationship between the weighted (stochastic) Prékopa-Leindler inequality and properties of (stochastic) parabolic equation on bounded domain, which is new even for deterministic case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.32288

Author: Lv, Guangying

Institution: Nanjing University of Information Science and Technology

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223701419

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