Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts

Antoine-Marie Bogso; Olivier Menoukeu Pamen

doi:10.30757/alea.v20-58

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arXiv · 2210.04694

Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts

Antoine-Marie Bogso·Olivier Menoukeu Pamen

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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.

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Antoine-Marie Bogso, Olivier Menoukeu Pamen. 2022-10-10. Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts. https://doi.org/10.30757/alea.v20-58

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