Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts
Abstract
We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied.
Keywords
Cite
@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}
}
Comments
25 pages. arXiv admin note: text overlap with arXiv:2112.00393