التفاصيل البيبلوغرافية
| العنوان: |
Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts. |
| المؤلفون: |
Bogso, Antoine-Marie, Pamen, Olivier Menoukeu |
| المصدر: |
ALEA. Latin American Journal of Probability & Mathematical Statistics; 2023, Vol. 20 Issue 2, p1537-1564, 28p |
| مصطلحات موضوعية: |
HYPERBOLIC differential equations, BROWNIAN motion, STATISTICAL physics in random environment, EMPIRICAL research, PARTIAL differential equations |
| مستخلص: |
We prove path-by-path uniqueness of solutions 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 SDEs 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 a spatial linear growth drift coefficient is also studied. [ABSTRACT FROM AUTHOR] |
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