Well-posedness of the deterministic transport equation with singular velocity field perturbed along fractional Brownian paths

Autor: Amine, Oussama, Mansouri, Abdol-Reza, Proske, Frank

Publikováno v: In Journal of Differential Equations 25 July 2023 362:106-172

A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling

Autor: Amine, Oussama, Coffie, Emmanuel, Harang, Fabian, Proske, Frank

In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a multi-dimensional fractional Brownian motion with Hurst parameter $H<1/2$.

Externí odkaz: http://arxiv.org/abs/1805.11435

C-infinity-regularization by Noise of Singular ODE's

Autor: Amine, Oussama, Baños, David, Proske, Frank

In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation with this noise with a highly irregular coefficient. We employ a new method to prove existenc

Externí odkaz: http://arxiv.org/abs/1710.05760

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Regularity properties of the stochastic flow of a skew fractional Brownian motion

Autor: Amine, Oussama, Baños, David, Proske, Frank Norbert

Publikováno v: Amine, Oussama Baños, David Proske, Frank Norbert . Regularity properties of the stochastic flow of a skew fractional Brownian motion. Infinite Dimensional Analysis Quantum Probability and Related Topics. 2020, 23(1)
Infinite Dimensional Analysis Quantum Probability and Related Topics

Externí odkaz: http://hdl.handle.net/10852/85078
https://www.duo.uio.no/bitstream/handle/10852/85078/2/Flow.pdf