具有不规则漂移的双曲型随机偏微分方程解的Malliavin可微性
概率论
2024-01-18 v2
摘要
我们证明了当漂移系数为具有空间线性增长的两种分量单调Borel可测函数之差时，双曲型随机偏微分方程解的路径逐路径唯一性。由布朗单驱动的SDE的Yamada-Watanabe原理可推导出此类方程的强唯一性，从而推广了[Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022]和[Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]中的结果。假设漂移全局有界，我们证明唯一强解是Malliavin可微的。具有空间线性增长漂移系数的情形也得到了研究。
引用
@article{arxiv.2210.04694,
title = {Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts},
author = {Antoine-Marie Bogso and Olivier Menoukeu Pamen},
journal= {arXiv preprint arXiv:2210.04694},
year = {2024}
}
备注
25 pages. arXiv admin note: text overlap with arXiv:2112.00393