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PreprintCC BY-SA 4.0arXiv

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

  • Guangying Lv
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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.

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Cite

BibTeXRIS
BibTeX
@misc{lv2026geometry,
  title = {{Geometry property of stochastic parabolic equations and Prékopa-Leindler inequality on bounded domains}},
  author = {Guangying Lv},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32288},
  eprint = {2610.32288},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32288},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Geometry property of stochastic parabolic equations and Prékopa-Leindler inequality on bounded domains
AU  - Guangying Lv
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32288
UR  - https://arxiv.org/abs/2610.32288
AB  - 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.
ER  -